What is (\partial)/(\partial x)(xsqrt((4-x^2))) ?

The answer to (\partial)/(\partial x)(xsqrt((4-x^2))) is (-2x^2+4)/(sqrt(4-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(xsqrt((4-x^2)))

\frac{\partial}{\partial x} (x (4 - x^{2}))

\frac{- 2 x ^{2} + 4}{4 - x ^{2}}

Solution steps

\frac{\partial}{\partial x} (x (4 - x^{2}))

Apply the Product Rule:

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

f = x, g = 4 - x^{2}

= \frac{\partial}{\partial x} (x) 4 - x^{2} + \frac{\partial}{\partial x} (4 - x^{2}) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (4 - x^{2}) = - \frac{x}{4 - x ^{2}}

= 1 \cdot 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) x

Simplify

1 \cdot 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) x : \frac{- 2 x ^{2} + 4}{4 - x ^{2}}

= \frac{- 2 x ^{2} + 4}{4 - x ^{2}}

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{2} e^{x}

y^{^{'}} - \frac{y}{x} = x cos (x)

\frac{d}{d x} (\frac{1}{4} x^{4} - 2 x^{2})

d x + e^{8 x} d y = 0

What is (\partial)/(\partial x)(xsqrt((4-x^2))) ?
The answer to (\partial)/(\partial x)(xsqrt((4-x^2))) is (-2x^2+4)/(sqrt(4-x^2))