How do you differentiate 3/4x^-(4/5)+3x^-pi34x−(45)+3x−π?

1 Answer
mason m
Sep 6, 2016

-3/5x^(-9/5)-3pix^(-pi-1)−35x−95−3πx−π−1

Explanation:

Here, we will be using the power rule. The power rule states that d/dx(x^n)=nx^(n-1)ddx(xn)=nxn−1. This is basically the same when the function has a constant multiplied by it: d/dx(ax^n)=anx^(n-1)ddx(axn)=anxn−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))ddx(34x−45)+ddx(3x−π)

=3/4(-4/5)x^(-4/5-1)+3(-pi)x^(-pi-1)=34(−45)x−45−1+3(−π)x−π−1

=-3/5x^(-9/5)-3pix^(-pi-1)=−35x−95−3πx−π−1

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