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10 cards from this deck
Differentiate composite functions (function within function)
dydx=f′(g(x))⋅g′(x)\frac{dy}{dx} = f'(g(x)) \cdot g'(x)dxdy=f′(g(x))⋅g′(x)
dydx=dydu⋅dudx\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}dxdy=dudy⋅dxdu
exe^xex
1x\frac{1}{x}x1
3cos(3x)3\cos(3x)3cos(3x)
Function wrapped within another function (not just multiplication)
f′(g(h(x)))⋅g′(h(x))⋅h′(x)f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x)f′(g(h(x)))⋅g′(h(x))⋅h′(x)
Differentiate outer, multiply by inner derivative
2xex2+22xe^{x^2+2}2xex2+2
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