What is the derivative of ln(2cos^4(θ)) ?

The derivative of ln(2cos^4(θ)) is -4tan(θ)

What is the first derivative of ln(2cos^4(θ)) ?

The first derivative of ln(2cos^4(θ)) is -4tan(θ)

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derivative of

ln (2 cos^{4} (θ))

- 4 tan (θ)

Solution steps

\frac{d}{d θ} (ln (2 cos^{4} (θ)))

Apply the chain rule:

\frac{1}{2 cos ^{4} ( θ )} \frac{d}{d θ} (2 cos^{4} (θ))

= \frac{1}{2 cos ^{4} ( θ )} \frac{d}{d θ} (2 cos^{4} (θ))

\frac{d}{d θ} (2 cos^{4} (θ)) = - 8 cos^{3} (θ) sin (θ)

= \frac{1}{2 cos ^{4} ( θ )} (- 8 cos^{3} (θ) sin (θ))

Simplify

\frac{1}{2 cos ^{4} ( θ )} (- 8 cos^{3} (θ) sin (θ)) : - 4 tan (θ)

= - 4 tan (θ)

(x e^{x})^{^{'}}

\frac{d y}{d x} = y^{3} x e^{x^{2}}, y (0) = 1

x \to 3 lim (4 x^{2} - 3 x + 2)

What is the derivative of ln(2cos^4(θ)) ?
The derivative of ln(2cos^4(θ)) is -4tan(θ)
What is the first derivative of ln(2cos^4(θ)) ?
The first derivative of ln(2cos^4(θ)) is -4tan(θ)