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Technique to differentiate composite functions.
dy/dx=f′(g(x))∗g′(x)dy/dx = f'(g(x)) * g'(x)dy/dx=f′(g(x))∗g′(x)
f′(g(x))f'(g(x))f′(g(x)) is the derivative of the outer function.
g′(x)g'(x)g′(x) is the derivative of the inner function.
dydx=dydu⋅dudx\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}dxdy=dudy⋅dxdu
Identify the outer and inner functions.
The derivative is n⋅x(n−1)n \cdot x^{(n-1)}n⋅x(n−1).
Multiply the derivatives of outer and inner functions.
dydx=3cos(3x)\frac{dy}{dx} = 3\cos(3x)dxdy=3cos(3x)
dydx=10x5x2+1\frac{dy}{dx} = \frac{10x}{5x^2 + 1}dxdy=5x2+110x
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