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BigorU [14]
3 years ago
5

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = ta

n(πx) (g(x), f(u)) = ___________ Find the derivative dy/dx. dy/dx = ___________
Mathematics
1 answer:
Irina-Kira [14]3 years ago
7 0

Answer:

The inner function is u = \pi x.

The outer function is f(u) = \tan{u}.

\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}

Step-by-step explanation:

The inner function is the one we apply the outer function to.

So

y = \tan{\pi x}

We apply the outer function tangent to \pi x.

So, the inner function is u = \pi x.

The outer function is f(u) = \tan{u}.

The derivative of a compositve function

y = f(u) in which u = g(x) is given by the following function.

y^{\prime} = f^{\prime}(u)*g^{\prime}(x)

So

f(u) = \tan{u}

f^{\prime}(u) = \sec^{2}{u}

u = g(x) = \pi x

g^{\prime}(x) = \pi

So

y^{\prime} = f^{\prime}(u)*g^{\prime}(x)

\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}

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