Question

How do you differentiate `3/4x^-(4/5)+3x^-pi`?

Answer 1

`-3/5x^(-9/5)-3pix^(-pi-1)`

Explanation:

Here, we will be using the power rule. The power rule states that `d/dx(x^n)=nx^(n-1)`. This is basically the same when the function has a constant multiplied by it: `d/dx(ax^n)=anx^(n-1)`.

Thus, taking the derivative of each part, we see that the function's derivative is:

`d/dx(3/4x^(-4/5))+d/dx(3x^(-pi))`

`=3/4(-4/5)x^(-4/5-1)+3(-pi)x^(-pi-1)`

`=-3/5x^(-9/5)-3pix^(-pi-1)`