What is the derivative of (1+cos^3(x^7))^{12} ?

The derivative of (1+cos^3(x^7))^{12} is -252x^6cos^2(x^7)sin(x^7)(1+cos^3(x^7))^{11}

What is the first derivative of (1+cos^3(x^7))^{12} ?

The first derivative of (1+cos^3(x^7))^{12} is -252x^6cos^2(x^7)sin(x^7)(1+cos^3(x^7))^{11}

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derivative of

(1 + cos^{3} (x^{7}))^{12}

- 252 x^{6} cos^{2} (x^{7}) sin (x^{7}) (1 + cos^{3} (x^{7}))^{11}

Solution steps

\frac{d}{d x} ((1 + cos^{3} (x^{7}))^{12})

Apply the chain rule:

12 (1 + cos^{3} (x^{7}))^{11} \frac{d}{d x} (1 + cos^{3} (x^{7}))

= 12 (1 + cos^{3} (x^{7}))^{11} \frac{d}{d x} (1 + cos^{3} (x^{7}))

\frac{d}{d x} (1 + cos^{3} (x^{7})) = - 21 x^{6} cos^{2} (x^{7}) sin (x^{7})

= 12 (1 + cos^{3} (x^{7}))^{11} (- 21 x^{6} cos^{2} (x^{7}) sin (x^{7}))

Simplify

= - 252 x^{6} cos^{2} (x^{7}) sin (x^{7}) (1 + cos^{3} (x^{7}))^{11}

\frac{\partial}{\partial x} (y^{3} sin (6 x))

f (x) = \frac{2}{3 x + 5}, (- 1, 1)

x \to 0 lim (\frac{x ^{2} + 7 x}{x})

\int (2 t + 3)^{- 3} d t

f (x) = \frac{2 x - 1}{x + 5}, at x = 4

What is the derivative of (1+cos^3(x^7))^{12} ?
The derivative of (1+cos^3(x^7))^{12} is -252x^6cos^2(x^7)sin(x^7)(1+cos^3(x^7))^{11}
What is the first derivative of (1+cos^3(x^7))^{12} ?
The first derivative of (1+cos^3(x^7))^{12} is -252x^6cos^2(x^7)sin(x^7)(1+cos^3(x^7))^{11}