What is the derivative of 3cos^{-3}(x) ?

The derivative of 3cos^{-3}(x) is (9sin(x))/(cos^4(x))

What is the first derivative of 3cos^{-3}(x) ?

The first derivative of 3cos^{-3}(x) is (9sin(x))/(cos^4(x))

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derivative of

3 cos^{- 3} (x)

\frac{9 sin ( x )}{cos ^{4} ( x )}

Solution steps

\frac{d}{d x} (3 cos^{- 3} (x))

Take the constant out:

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

= 3 \frac{d}{d x} (cos^{- 3} (x))

Apply the chain rule:

- \frac{3}{( cos ( x ) ) ^{4}} \frac{d}{d x} (cos (x))

= - \frac{3}{( cos ( x ) ) ^{4}} \frac{d}{d x} (cos (x))

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

= 3 (- \frac{3}{( cos ( x ) ) ^{4}} (- sin (x)))

Simplify

3 (- \frac{3}{cos ^{4} ( x )} (- sin (x))) : \frac{9 sin ( x )}{cos ^{4} ( x )}

= \frac{9 sin ( x )}{cos ^{4} ( x )}

What is the derivative of 3cos^{-3}(x) ?
The derivative of 3cos^{-3}(x) is (9sin(x))/(cos^4(x))
What is the first derivative of 3cos^{-3}(x) ?
The first derivative of 3cos^{-3}(x) is (9sin(x))/(cos^4(x))