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Popular >

derivative of 2cos^{12}(x)

Solution

\frac{d}{d x} (2 cos^{12} (x))

Solution

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

Solution steps

\frac{d}{d x} (2 cos^{12} (x))

Take the constant out:

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

= 2 \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)

= 2 \cdot 12 (cos (x))^{11} (- sin (x))

Simplify

= - 24 cos^{11} (x) sin (x)

Popular Examples

limit as x approaches infinity of (5)\sqrt[6666]{6}

limit as x approaches 0 of y^x

x \to 0 lim (y^{x})

limit as x approaches-1+of (x+1)/(x^3+1)

x \to - 1 + lim (\frac{x + 1}{x ^{3} + 1})

y^{''}+6y^'+25y=100,y(0)=0,y^'(0)=0

y^{^{''}} + 6 y^{^{'}} + 25 y = 100, y (0) = 0, y^{^{'}} (0) = 0

(\partial)/(\partial x)(-e^xln(y))

\frac{\partial}{\partial x} (- e^{x} ln (y))

Frequently Asked Questions (FAQ)

What is the derivative of 2cos^{12}(x) ?
The derivative of 2cos^{12}(x) is -24cos^{11}(x)sin(x)
What is the first derivative of 2cos^{12}(x) ?
The first derivative of 2cos^{12}(x) is -24cos^{11}(x)sin(x)