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f(x)=|x|
|x| = sqrt(x^2)
f(x) = sqrt (x^2)
f'(x)=1/2sqrt(x^2) d/dx(x^2)
f'(x) = 2x /2sqrt(x^2)
f'(x) = x/sqrt(x^2)
f'(x)= x /|x|
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Note: d/dx [sqrt(x^2] = d/dx [x^(1/2)] =(1/2)x^(-1/2)=1/2x^(1/2)=1/2sqrt(x)
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How can you know that a value is the minimum of a function?
When the first derivative of the function is equal to zero and the second derivative is positive.
What is the derivative of modulus of x?
Well.. this is the formula to get the derivative of the modulus - d|f(x)|/dx = [ |f(x)|/f(x) ] * f'(x)
Is the first derivative of a function is a constant then its graph is?
A line. The derivative of a function is its slope. If the slope is a constant then the graph is a line.
How do you find the derivative of y equals 7e-6x?
13
What is a derivative graph?
A derivative graph tracks the slope of a function.
What is the second derivative of a function's indefinite integral?
well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.
What is the function if the first derivative of a function is a constant?
A linear function, for example y(x) = ax + b has the first derivative a.
How do you find second derivative of a function?
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
How can you know that a value is the minimum of a function?
When the first derivative of the function is equal to zero and the second derivative is positive.
What is the significance of the first derivative of a function to be a constant?
If the first derivative if a function is a constant that the original function has only one slope across its entire domain, so it is a line.
What characteristics of the graph of a function by using the concept of differentiation first and second derivatives?
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
Where the graph of a function equals the value zero?
you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.
How do you trace a curve in differential calculus?
To trace a curve using differential calculus, you use the fact that the first derivative of the function is the slope of the curve, and the second derivative is the slope of the first derivative. What this means is that the zeros (roots) of the first derivative give the extrema (max or min) or an inflection point of the function. Evaluating the first derivative function at either side of the zero will tell you whether it is a min/max or inflection point (i.e. if the first derivative is negative on the left of the zero and positive on the right, then the curve has a negative slope, then a min, then a positive slope). The second derivative will tell you if the curve is concave up or concave down by evaluating if the second derivative function is positive or negative before and after extrema.
What is the derivative of modulus of x?
Well.. this is the formula to get the derivative of the modulus - d|f(x)|/dx = [ |f(x)|/f(x) ] * f'(x)
What is the difference between nonlinear and linear functions?
Linear function:No variable appears in the function to any power other than 1.A periodic input produces no new frequencies in the output.The function's first derivative is a number; second derivative is zero.The graph of the function is a straight line.Non-linear function:A variable appears in the function to a power other than 1.A periodic function at the input produces new frequencies in the output.The function's first derivative is a function; second derivative is not zero.The graph of the function is not a straight line.
Is modulus function one one?
No.
How do you get the second derivative of potential energy?
The same way you get the second derivative from any function. Assuming you have a function that expresses potential energy as a function of time, or perhaps as a function of position, you take the derivate of this function. This will give you another function. Then, you take the derivate of this derivative, to get the second derivative.
