What is the derivative of 5e^{4x}-cos^2(2e^x) ?

The derivative of 5e^{4x}-cos^2(2e^x) is 20e^{4x}+4e^xcos(2e^x)sin(2e^x)

What is the first derivative of 5e^{4x}-cos^2(2e^x) ?

The first derivative of 5e^{4x}-cos^2(2e^x) is 20e^{4x}+4e^xcos(2e^x)sin(2e^x)

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\frac{d}{d x} (5 e^{4 x} - cos^{2} (2 e^{x}))

20 e^{4 x} + 4 e^{x} cos (2 e^{x}) sin (2 e^{x})

Solution steps

\frac{d}{d x} (5 e^{4 x} - cos^{2} (2 e^{x}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (5 e^{4 x}) - \frac{d}{d x} (cos^{2} (2 e^{x}))

\frac{d}{d x} (5 e^{4 x}) = 20 e^{4 x}

\frac{d}{d x} (cos^{2} (2 e^{x})) = - 4 e^{x} cos (2 e^{x}) sin (2 e^{x})

= 20 e^{4 x} - (- 4 e^{x} cos (2 e^{x}) sin (2 e^{x}))

Simplify

= 20 e^{4 x} + 4 e^{x} cos (2 e^{x}) sin (2 e^{x})

\int sin^{2} (2 θ) d θ

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} + 12 y = 0

\frac{d}{d x} (\frac{4}{3} x^{3} + 2)

\int_{0}^{\infty} \frac{7}{x ^{2} + 1} d x

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What is the derivative of 5e^{4x}-cos^2(2e^x) ?
The derivative of 5e^{4x}-cos^2(2e^x) is 20e^{4x}+4e^xcos(2e^x)sin(2e^x)
What is the first derivative of 5e^{4x}-cos^2(2e^x) ?
The first derivative of 5e^{4x}-cos^2(2e^x) is 20e^{4x}+4e^xcos(2e^x)sin(2e^x)