en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(8e^{ysqrt(x)}-x^2y^3)

Solution

\frac{\partial}{\partial x} (8 e^{y x} - x^{2} y^{3})

Solution

\frac{4 y e ^{y x}}{x} - 2 y^{3} x

Solution steps

\frac{\partial}{\partial x} (8 e^{y x} - x^{2} y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (8 e^{y x}) - \frac{\partial}{\partial x} (x^{2} y^{3})

\frac{\partial}{\partial x} (8 e^{y x}) = \frac{4 y e ^{y x}}{x}

\frac{\partial}{\partial x} (x^{2} y^{3}) = 2 y^{3} x

= \frac{4 y e ^{y x}}{x} - 2 y^{3} x

Popular Examples

integral of 10e^{-10x}

\int 10 e^{- 10 x} d x

integral of-8/pi x

\int - \frac{8}{π} x d x

tangent of f(x)= 2/(1+e^{-x)},(0,1)tangent of

f (x) = \frac{2}{1 + e ^{- x}}, (0, 1)

x^{^{'}} = (x - 17)^{2}

tangent of f(x)= 7/(x+8),(5, 7/13)tangent of

f (x) = \frac{7}{x + 8}, (5, \frac{7}{13})

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(8e^{ysqrt(x)}-x^2y^3) ?
The answer to (\partial)/(\partial x)(8e^{ysqrt(x)}-x^2y^3) is (4ye^{ysqrt(x)})/(sqrt(x))-2y^3x