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10 questions from this quiz
Differentiating composite functions
One function's output used as another's input
u=4x3−2x+7u = 4x^3 - 2x + 7u=4x3−2x+7
What operation is performed last?
dydx=dydu×dudx\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}dxdy=dudy×dxdu
ddx([f(x)]n)=n[f(x)]n−1×f′(x)\frac{d}{dx}([f(x)]^n) = n[f(x)]^{n-1} \times f'(x)dxd([f(x)]n)=n[f(x)]n−1×f′(x)
Bring down power, reduce by 1, multiply by f′(x)f'(x)f′(x)
Substitute back to express answer in xxx
Convert them to index form
Yes, it works for fractional exponents
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