What is the derivative of sin^5(3x^2-x+13) ?

The derivative of sin^5(3x^2-x+13) is 5sin^4(3x^2-x+13)cos(3x^2-x+13)(6x-1)

What is the first derivative of sin^5(3x^2-x+13) ?

The first derivative of sin^5(3x^2-x+13) is 5sin^4(3x^2-x+13)cos(3x^2-x+13)(6x-1)

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derivative of

sin^{5} (3 x^{2} - x + 13)

5 sin^{4} (3 x^{2} - x + 13) cos (3 x^{2} - x + 13) (6 x - 1)

Solution steps

\frac{d}{d x} (sin^{5} (3 x^{2} - x + 13))

Apply the chain rule:

5 (sin (3 x^{2} - x + 13))^{4} \frac{d}{d x} (sin (3 x^{2} - x + 13))

= 5 (sin (3 x^{2} - x + 13))^{4} \frac{d}{d x} (sin (3 x^{2} - x + 13))

\frac{d}{d x} (sin (3 x^{2} - x + 13)) = cos (3 x^{2} - x + 13) (6 x - 1)

= 5 (sin (3 x^{2} - x + 13))^{4} cos (3 x^{2} - x + 13) (6 x - 1)

Simplify

= 5 sin^{4} (3 x^{2} - x + 13) cos (3 x^{2} - x + 13) (6 x - 1)

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

(5 x + 3) + (5 y - 5) y^{^{'}} = 0

\int csc (x) d x

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

\int (x + 1)^{10} d x

What is the derivative of sin^5(3x^2-x+13) ?
The derivative of sin^5(3x^2-x+13) is 5sin^4(3x^2-x+13)cos(3x^2-x+13)(6x-1)
What is the first derivative of sin^5(3x^2-x+13) ?
The first derivative of sin^5(3x^2-x+13) is 5sin^4(3x^2-x+13)cos(3x^2-x+13)(6x-1)