What is the derivative of sin^5(x^2+1^7) ?

The derivative of sin^5(x^2+1^7) is 70xsin^{34}(x^2+1)cos(x^2+1)

What is the first derivative of sin^5(x^2+1^7) ?

The first derivative of sin^5(x^2+1^7) is 70xsin^{34}(x^2+1)cos(x^2+1)

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\frac{d}{d x} (sin^{5} (x^{2} + 1)^{7})

70 x sin^{34} (x^{2} + 1) cos (x^{2} + 1)

Solution steps

\frac{d}{d x} ((sin^{5} (x^{2} + 1))^{7})

Simplify

(sin^{5} (x^{2} + 1))^{7} : sin^{35} (x^{2} + 1)

= \frac{d}{d x} (sin^{35} (x^{2} + 1))

Apply the chain rule:

35 (sin (x^{2} + 1))^{34} \frac{d}{d x} (sin (x^{2} + 1))

= 35 (sin (x^{2} + 1))^{34} \frac{d}{d x} (sin (x^{2} + 1))

\frac{d}{d x} (sin (x^{2} + 1)) = cos (x^{2} + 1) \cdot 2 x

= 35 (sin (x^{2} + 1))^{34} cos (x^{2} + 1) \cdot 2 x

Simplify

= 70 x sin^{34} (x^{2} + 1) cos (x^{2} + 1)

\int 3 x^{2} e^{4 x} d x

\int \frac{( x + 1 )}{x x - 2} d x

\frac{\partial}{\partial x} (cos (x) - x cos (y) - y)

x \to - 2 - lim (2 - x)

4 x \frac{d y}{d x} = 2 x e^{x} - 4 y + 6 x^{2}

What is the derivative of sin^5(x^2+1^7) ?
The derivative of sin^5(x^2+1^7) is 70xsin^{34}(x^2+1)cos(x^2+1)
What is the first derivative of sin^5(x^2+1^7) ?
The first derivative of sin^5(x^2+1^7) is 70xsin^{34}(x^2+1)cos(x^2+1)