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If
f(x)=ex2,f(x) = e^{x^2},f(x)=ex2,
what is the correct expression for f′(x)?f'(x)?f′(x)?
Which statement(s) are true?
A. If f(x)=x2,f(x) = x^2,f(x)=x2, then f′(x)=2x.f'(x) = 2x.f′(x)=2x.
B. If f′(x)=2x,f'(x) = 2x,f′(x)=2x, then f(x)=x2.f(x) = x^2.f(x)=x2.
True or False?
Suppose fff is a differentiable function on the interval (a,b).(a,b).(a,b). If fff is decreasing on (a,b),(a,b),(a,b), then f′<0f'<0f′<0 on (a,b).(a,b).(a,b).
∫−111x2 dx=x−2+1−2+1∣−11=−1−1=−2.\displaystyle \int_{-1}^1 \frac{1}{x^2} \,dx = \left . \dfrac{x^{-2+1}}{-2+1} \right |_{-1}^1 = -1 -1 = -2. ∫−11x21dx=−2+1x−2+1∣∣∣∣−11=−1−1=−2.
If f(x)=2x,f(x) = 2^x,f(x)=2x, then f′(x)=x⋅2x−1.f'(x) = x\cdot 2^{x-1}.f′(x)=x⋅2x−1.
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