Question

Differentiate y = cos (a^3 + x^3)

Answer 1

with respect to?

Answer 2

Assuming differentiation with respect to \(x\), let\[f(x)=\cos x\]and\[g(x)=a^3+x^3.\]Then\[y=f(g(x))\]and\[y'=f'(g(x))g'(x).\]We know that\[f'(x)=-\sin x\]and\[g'(x)=3x^2.\]Therefore,\[y'=-3x^2\sin(a^3+x^3).\]

Answer 3

what about a^x = a^x ln a ?

Answer 4

that's where i got screwed

Answer 5

\[y=a^{f(x)}\]
\[y'=a^{f(x)}*f'(x)*\ln a\]