What is the derivative of cos^{12}(x) ?

The derivative of cos^{12}(x) is -12cos^{11}(x)sin(x)

What is the first derivative of cos^{12}(x) ?

The first derivative of cos^{12}(x) is -12cos^{11}(x)sin(x)

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\frac{d}{d x} (cos^{12} (x))

- 12 cos^{11} (x) sin (x)

Solution steps

\frac{d}{d x} (cos^{12} (x))

Apply the chain rule:

12 (cos (x))^{11} \frac{d}{d x} (cos (x))

= 12 (cos (x))^{11} \frac{d}{d x} (cos (x))

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

= 12 (cos (x))^{11} (- sin (x))

Simplify

= - 12 cos^{11} (x) sin (x)

5 t + \frac{7}{t}

\int \frac{1}{3 ^{- x}} d x

\int cos (5 x + 7) d x

f (x) = \frac{x ^{2} - 2}{x ^{2} + 2}

\frac{\partial}{\partial x} ((x + y) ln (\frac{x}{y}))

What is the derivative of cos^{12}(x) ?
The derivative of cos^{12}(x) is -12cos^{11}(x)sin(x)
What is the first derivative of cos^{12}(x) ?
The first derivative of cos^{12}(x) is -12cos^{11}(x)sin(x)