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Find dy/dx of y=1/x. It may be simpler for you to examine the equation y=x^-1. This equation is the exact same as y=1/x. Therefore just multiply -1 by x and subtract 1 from the exponent giving you -x^-2 or y=-(1/x^2).
You can also do it through quotient rules. Therefore take the derivative of the top 1 which = 0 and multiply that by the bottom X which will give you 0. Then subtract the derivative of the bottom x this equals 1 and multiply it by the top (1). Put this all over the bottom squared. Which leads to -1/x^2.
y=1/x = y=x^-1 = -x^-2 = -(1/x^2)=dy/dx
or
y=1/x = ((0*x)-(1*1)/x^2 = dy/dx=-1/x^2
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What is the derivative of x divided by y?
You have to specify more information than that. If y is an independent variable and you're talking about the derivative with respect to x, it would be 1/y.
What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
Derivative of x 1?
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What is the derivative of x divided by 2?
x/2 is the same as (1/2) times x. Thus, you can use the formula for a constant factor.
What is the second derivative of square root x?
It is negative one divided by 4 multiplied by x to the power of 1.5 -1/(4(x^1.5))
What is the derivative of x divided by 3?
The derivative of x divided by 3 is 1/3. This can be found using the power rule of differentiation, where the derivative of x^n is nx^(n-1). In this case, x can be written as x^1, so the derivative is 1(1/3)*x^(1-1) = 1/3.
What is the derivative of 1 divided by root x?
(1/2(x^-1/2))/x
What is the derivative of 1 divided by 1 plus x?
2
What is the derivative of 1 divided by x to the third power?
1 divided by x to the third power equals x to the negative third. The derivative of x to the negative third is minus three x to the negative fourth.
What is the derivative of cos x sin x divided by cos x sin x?
(cos x sin x) / (cos x sin x) = 1. The derivative of a constant, such as 1, is zero.
What is the derivative of 1 divided by fx under the conditions that fx is differentiable and fx cannot be 0?
Negative the derivative of f(x), divided by f(x) squared. -f'(x) / f²(x)
What is the derivative of ln1 divided by x?
Given y=ln(1/x) y'=(1/(1/x))(-x-2)=(1/(1/x))(1/x2)=x/x2=1/x Use the chain rule. The derivative of ln(x) is 1/x. Instead of just "x" inside the natural log function, it's "1/x". Since the inside of the function is not x, the derivative must be multiplied by the derivative of the inside of the function. So it's 1/(1/x) [the derivative of the outside function, natural log] times -x-2=1/x2 [the derivative of the inside of the function, 1/x] This all simplifies to 1/x So the derivative of ln(1/x) is 1/x
What is the derivative of 5 divided by x?
Well if you have 5/X then you can rewrite this like 5x-1. And the derivative to that is -5x-2 and that can be rewrote to: -(5/x2).
What is the derivative of 1 over x?
Derivative of 1/x 1/x = x-1 Take the derivative (-1)x(-1-1) = -x-2 = 1/x2
What is the derivative of x divided by y?
You have to specify more information than that. If y is an independent variable and you're talking about the derivative with respect to x, it would be 1/y.
What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
Derivative of x 1?
the derivative of 1x would be 1 the derivative of x to the power of 1 would be 1. the derivative of x+1 would be 1 the derivative of x-1 would be 1 im not sure what you are asking, but however you put it, it's 1.
