Property 6
Derivative of Multiplication of Two Functions
\([f(x)\cdot g(x)]'=f'(x)\cdot g(x)+g'(x)\cdot f(x)\)
1.
\(f(x)=(x^2-1)\cdot(x+1)\)
\(\Rightarrow f'(x)=?\)
2.
\(f(x)=(x^2-x)\cdot(x+1)\)
\(\Rightarrow f'(x)=?\)
3.
\(f(x)=2x^2\cdot(x^2-1)\)
\(\Rightarrow f'(x)=?\)
4.
\(f(x)=(4x^2-1)\cdot(x^2-1)\)
\(\Rightarrow f'(1)=?\)
5.
\(f(x)=(x^3+1)\cdot(x-1)\)
\(\Rightarrow f'(2)=?\)
6.
\(f(x)=\sin x\cdot(x^3-1)\)
\(\Rightarrow f'(x)=?\)
7.
\(f(x)=(x-1)\cdot(x-2)\cdot(x-3)\)
\(\Rightarrow f'(2)=?\)
8.
\(f(x)=x\cdot\cos x\)
\(\Rightarrow f'(x)=?\)
9.
\(f(x)=\sqrt x\cdot\sin x\)
\(\Rightarrow f'(x)=?\)
10.
\(f(x)=x^3\cdot2^x\)
\(\Rightarrow f'(x)=?\)
11.
\(f(x)=x^2\cdot\sin x\)
\(\Rightarrow f'\left(\samefrac{\pi}{2}\right)=?\)
12.
\(f(x)=e^x\cdot\sin x\)
\(\Rightarrow f'(0)=?\)