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

The derivative of 5cos^{-4}(x) is (20sin(x))/(cos^5(x))

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

The first derivative of 5cos^{-4}(x) is (20sin(x))/(cos^5(x))

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

\frac{20 sin ( x )}{cos ^{5} ( x )}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

= 5 (- \frac{4}{( cos ( x ) ) ^{5}} (- sin (x)))

Simplify

5 (- \frac{4}{cos ^{5} ( x )} (- sin (x))) : \frac{20 sin ( x )}{cos ^{5} ( x )}

= \frac{20 sin ( x )}{cos ^{5} ( x )}

\int \frac{e ^{2 x}}{e ^{2 x} - 1} d x

\frac{d}{d x} (sin (x + π))

x^{2} e^{x}

n = 0 \sum \infty tan (n)

\int \frac{csc ^{2} ( 2 x )}{cot ^{5} ( 2 x )} d x

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