- #1
flower321
- 11
- 0
if (d/dx) cos(x) = -sin(x) then (d/d{1/x}) cos(x) = ? i.e. the derivative of cos(x) with respect to 1/x
"Derivative with respect to 1/x" refers to the derivative of a function with respect to the variable 1/x. This means that the derivative is being taken with respect to the reciprocal of x, or the inverse of x.
To calculate the derivative with respect to 1/x, you can use the chain rule. First, rewrite the function in terms of 1/x. Then, take the derivative of the function with respect to 1/x, and multiply it by the derivative of 1/x with respect to x.
The derivative with respect to 1/x is useful in many applications, such as in physics and engineering. It can help determine rates of change and optimize functions that involve inverse relationships. It can also be used to solve problems involving logarithms and exponential functions.
The derivative with respect to x represents the instantaneous rate of change of a function with respect to the variable x. On the other hand, the derivative with respect to 1/x represents the instantaneous rate of change of a function with respect to the reciprocal of x, or the inverse of x.
Yes, there are some special rules that can make it easier to calculate the derivative with respect to 1/x. For example, the derivative of 1/x is equal to -1/x^2. Additionally, the chain rule can be used to simplify the calculation of the derivative with respect to 1/x.