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If f(x)=3x2f(x) = 3x^2f(x)=3x2, which of the following is equal to f′(5)f'(5)f′(5)?
If f(x)=ex2f(x) = e^{x^2}f(x)=ex2, which of the following is equal to f′(1)f'(1)f′(1)?
Hint. If f(x)=ex,f(x) = e^{x},f(x)=ex, then f′(x)=ex.f'(x) = e^{x}.f′(x)=ex.
If q(x)=x2exq(x) = \frac{x^2}{e^x}q(x)=exx2, which of the following is equal to q′(x)q'(x)q′(x)?
Hint: If g(x)=exg(x) = e^xg(x)=ex, then g′(x)=ex.g'(x) = e^x.g′(x)=ex.
If h(x)=(x3+x2)(5x+1)h(x) = \color{#3D99F6}{(x^3 + x^2)}\color{#D61F06}{(5x + 1)}h(x)=(x3+x2)(5x+1), which of the following is equal to h′(x)h'(x)h′(x)?
A.h′(x)=(3x2+2x)⋅(5).A. h'(x) = \color{#3D99F6}{(3x^2 + 2x)}\cdot \color{#D61F06}{(5)}.A.h′(x)=(3x2+2x)⋅(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)}.B.h′(x)=(x3+x2)⋅(5x+1)+(3x2+2x)⋅(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)}.C.h′(x)=(3x2+2x)⋅(5x+1)+(x3+x2)⋅(5).
(f□g)′=f′□g′(f \square g)' = f' \square g'(f□g)′=f′□g′
Which operators could replace the square to make a statement that is true for all differentiable functions fff and ggg?
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