Property 10
Derivative of Composite Function
\(\boxed{[f(g(x))]'=f'(g(x))\cdot g'(x)}\)
\(f(x)=[g(x)]^n\Rightarrow f'(x)=n\cdot[g(x)]^{n-1}\cdot g'(x)\)
\(f(x)=a^{g(x)}\Rightarrow f'(x)=a^{g(x)}\cdot\ln a\cdot g'(x)\)
\(f(x)=\sin(g(x))\Rightarrow f'(x)=\cos(g(x))\cdot g'(x)\)
\(f(x)=\cos(g(x))\Rightarrow f'(x)=-\sin(g(x))\cdot g'(x)\)
\(f(x)=\log_a g(x)\Rightarrow f'(x)=\samefrac{g'(x)}{g(x)\cdot\ln a}\)
\(f(x)=\ln(g(x))\Rightarrow f'(x)=\samefrac{g'(x)}{g(x)}\)
1.
\(f(x)=(x^2+x)^3\)
\(\Rightarrow f'(x)=?\)
2.
\(f(x)=(x^2-x+1)^5\)
\(\Rightarrow f'(x)=?\)
3.
\(f(x)=(x^2-2)^2+2x\)
\(\Rightarrow f'(2)=?\)
4.
\(f(x)=\sqrt{x+2}\)
\(\Rightarrow f'(2)=?\)
5.
\(f(x)=\sqrt{x^2+7}\)
\(\Rightarrow f'(3)=?\)
6.
\(f(x)=\sin^2x\)
\(\Rightarrow f'(x)=?\)
7.
\(f(x)=e^{2x}\)
\(\Rightarrow f'(x)=?\)
8.
\(f(x)=3^{(x^3)}\)
\(\Rightarrow f'(x)=?\)
9.
\(f(x)=e^{x^2-4}\)
\(\Rightarrow f'(2)=?\)
10.
\(f(x)=\ln(x+3)\)
\(\Rightarrow f'(x)=?\)