Calculus

Differentiation Rules

Differentiation Rules Warmup

         

If f(x)=3x2f(x) = 3x^2, which of the following is equal to f(5)f'(5)?

If f(x)=ex2f(x) = e^{x^2}, which of the following is equal to f(1)f'(1)?

Hint. If f(x)=ex,f(x) = e^{x}, then f(x)=ex.f'(x) = e^{x}.

If q(x)=x2exq(x) = \frac{x^2}{e^x}, which of the following is equal to q(x)q'(x)?

Hint: If g(x)=exg(x) = e^x, then g(x)=ex.g'(x) = e^x.

If h(x)=(x3+x2)(5x+1)h(x) = \color{#3D99F6}{(x^3 + x^2)}\color{#D61F06}{(5x + 1)}, which of the following is equal to h(x)h'(x)?

A.h(x)=(3x2+2x)(5).A. h'(x) = \color{#3D99F6}{(3x^2 + 2x)}\cdot \color{#D61F06}{(5)}.

B.h(x)=(x3+x2)(5x+1)+(3x2+2x)(5).B. h'(x) = \color{#3D99F6}{(x^3 + x^2)}\cdot \color{#D61F06}{(5x + 1)} + \color{#3D99F6}{(3x^2+2x)}\cdot \color{#D61F06}{(5)}.

C.h(x)=(3x2+2x)(5x+1)+(x3+x2)(5).C. h'(x) = \color{#3D99F6}{(3x^2 + 2x)}\cdot \color{#D61F06}{(5x + 1)} + \color{#3D99F6}{(x^3+x^2)}\cdot \color{#D61F06}{(5)}.

(fg)=fg(f \square g)' = f' \square g'

Which operators could replace the square to make a statement that is true for all differentiable functions ff and gg?

×

Problem Loading...

Note Loading...

Set Loading...