en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of xsinh(x^2)

Solution

\frac{d}{d x} (x sinh (x^{2}))

Solution

sinh (x^{2}) + 2 x^{2} cosh (x^{2})

Solution steps

\frac{d}{d x} (x sinh (x^{2}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sinh (x^{2})

= \frac{d x}{d x} sinh (x^{2}) + \frac{d}{d x} (sinh (x^{2})) x

\frac{d x}{d x} = 1

\frac{d}{d x} (sinh (x^{2})) = cosh (x^{2}) \cdot 2 x

= 1 \cdot sinh (x^{2}) + cosh (x^{2}) \cdot 2 xx

Simplify

1 \cdot sinh (x^{2}) + cosh (x^{2}) \cdot 2 xx : sinh (x^{2}) + 2 x^{2} cosh (x^{2})

= sinh (x^{2}) + 2 x^{2} cosh (x^{2})

Popular Examples

integral of 1/(x^3sqrt(x^2-16))

\int \frac{1}{x ^{3} x ^{2} - 16} d x

derivative of f(x)=sin(2x)+2cos(x)derivative of

f (x) = sin (2 x) + 2 cos (x)

limit as x approaches-4-of |x+4|-2x

x \to - 4 - lim (∣ x + 4 ∣ - 2 x)

integral from 120 to 150 of e^{-x/(100)}

\int_{120}^{150} e^{- \frac{x}{100}} d x

integral from 1 to infinity of 2/(x^2)

\int_{1}^{\infty} \frac{2}{x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of xsinh(x^2) ?
The derivative of xsinh(x^2) is sinh(x^2)+2x^2cosh(x^2)
What is the first derivative of xsinh(x^2) ?
The first derivative of xsinh(x^2) is sinh(x^2)+2x^2cosh(x^2)