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

1 Answer
mason m
Sep 6, 2016

#-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)#

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