Question

f(x)=(7x^1/4)((x^3)−10)

What's f'(3)?

Answer 1

So you have \[f(x)=(7x ^{1/4})(x ^{3}-10)\]Do you know how to do the product rule for derivatives?

Answer 2

I've been trying, but I just can't get it.

Answer 3

Sorry my computer is acting stupid....... give me a sec

Answer 4

So since the product rule is uv'+vu', just make one of the terms u and the other terms v so\[u=7x ^{1/4}\]and\[v=x ^{3}-10\]Then do the derivative of u and v according to the product rule\[u*v'+v*u'=(7x ^{1/4})(3x ^{2})+(x ^{3}-10)(\frac{ 7 }{ 4 }x ^{-3/4})\]Then if you want, you can simplify here or just plug in 3 for x since that is already the derivative.