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

The derivative of sin^5((x^2+1^7)) is 70xsin^4((x^2+1)^7)cos((x^2+1)^7)(x^2+1)^6

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

The first derivative of sin^5((x^2+1^7)) is 70xsin^4((x^2+1)^7)cos((x^2+1)^7)(x^2+1)^6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

70 x sin^{4} ((x^{2} + 1)^{7}) cos ((x^{2} + 1)^{7}) (x^{2} + 1)^{6}

Solution steps

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

Apply the chain rule:

5 (sin ((x^{2} + 1)^{7}))^{4} \frac{d}{d x} (sin ((x^{2} + 1)^{7}))

= 5 (sin ((x^{2} + 1)^{7}))^{4} \frac{d}{d x} (sin ((x^{2} + 1)^{7}))

\frac{d}{d x} (sin ((x^{2} + 1)^{7})) = cos ((x^{2} + 1)^{7}) \cdot 14 x (x^{2} + 1)^{6}

= 5 (sin ((x^{2} + 1)^{7}))^{4} cos ((x^{2} + 1)^{7}) \cdot 14 x (x^{2} + 1)^{6}

Simplify

= 70 x sin^{4} ((x^{2} + 1)^{7}) cos ((x^{2} + 1)^{7}) (x^{2} + 1)^{6}

\int 6 x cos (x^{2}) d x

\frac{\partial}{\partial x} (x^{8} + 5 x y^{9})

\frac{\partial}{\partial y} (x e^{x^{2} + y^{2}})

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

x \to 0 lim (8^{- x})

What is the derivative of sin^5((x^2+1^7)) ?
The derivative of sin^5((x^2+1^7)) is 70xsin^4((x^2+1)^7)cos((x^2+1)^7)(x^2+1)^6
What is the first derivative of sin^5((x^2+1^7)) ?
The first derivative of sin^5((x^2+1^7)) is 70xsin^4((x^2+1)^7)cos((x^2+1)^7)(x^2+1)^6