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The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]
For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))
So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).
Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}
So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)
What else can I help you with?
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
What is the domain of logarithm and exponential function?
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
What are some characteristics of the graph of an exponential function?
An exponential function is a nonlinear function in the form y=ab^x, where a isn't equal to zero. In a table, consecutive output values have a common ratio. a is the y-intercept of the exponential function and b is the rate of growth/decay.
Can a exponential function be a negative number?
Well -x^3/4 would be exponential
A function takes the exponential function's output and returns the exponential function's input?
A __________ function takes the exponential function's output and returns the exponential function's input.
What is the parent function for the exponential function?
The parent function of the exponential function is ax
How do we differentiate between a quadratic equation and an exponential equation?
a quadratic equation must be in this form ax^2+bx+c=0 (can either be + or -) an exponential just means that the function grows at an exponential rate f(x)=x^2 or x^3
Is the inverse of an exponential function the quadratic function?
No. The inverse of an exponential function is a logarithmic function.
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
A logarithmic function takes the exponential function's output and returns the exponential function's?
input
What is a relation which are exponential function?
Exponential relationship!
Is y equals x4 an exponetial function?
If the question is, Is y = x4 an exponential function ? then the answer is no.An exponential function is one where the variable appears as an exponent.So, y = 4x is an exponential function.
How do you change an exponential functions to a logarithmic function?
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.
Example of fundamental difference between a polynomial function and an exponential function?
fundamental difference between a polynomial function and an exponential function?
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
Does a linear function increase faster than an exponential function?
No, a linear function does not increase faster than an exponential function. While linear functions grow at a constant rate, exponential functions grow at an increasing rate, meaning that as the input value increases, the output of the exponential function will eventually surpass that of the linear function. For sufficiently large values of the input, the exponential function will outpace the linear function significantly.
