What is the derivative of sin^{12}(3x^4-x) ?

The derivative of sin^{12}(3x^4-x) is 12sin^{11}(3x^4-x)cos(3x^4-x)(12x^3-1)

What is the first derivative of sin^{12}(3x^4-x) ?

The first derivative of sin^{12}(3x^4-x) is 12sin^{11}(3x^4-x)cos(3x^4-x)(12x^3-1)

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\frac{d}{d x} (sin^{12} (3 x^{4} - x))

12 sin^{11} (3 x^{4} - x) cos (3 x^{4} - x) (12 x^{3} - 1)

Solution steps

\frac{d}{d x} (sin^{12} (3 x^{4} - x))

Apply the chain rule:

12 (sin (3 x^{4} - x))^{11} \frac{d}{d x} (sin (3 x^{4} - x))

= 12 (sin (3 x^{4} - x))^{11} \frac{d}{d x} (sin (3 x^{4} - x))

\frac{d}{d x} (sin (3 x^{4} - x)) = cos (3 x^{4} - x) (12 x^{3} - 1)

= 12 (sin (3 x^{4} - x))^{11} cos (3 x^{4} - x) (12 x^{3} - 1)

Simplify

= 12 sin^{11} (3 x^{4} - x) cos (3 x^{4} - x) (12 x^{3} - 1)

\frac{d y}{d x} = \frac{( 2 + y ) ^{2}}{2 x - 1}

3 t^{2} - 9 t

(4 x + 5)^{\frac{1}{5}}

arccos (\frac{x}{5})

\int \frac{4 x}{x ^{2} + 5} d x

What is the derivative of sin^{12}(3x^4-x) ?
The derivative of sin^{12}(3x^4-x) is 12sin^{11}(3x^4-x)cos(3x^4-x)(12x^3-1)
What is the first derivative of sin^{12}(3x^4-x) ?
The first derivative of sin^{12}(3x^4-x) is 12sin^{11}(3x^4-x)cos(3x^4-x)(12x^3-1)