What is the derivative of xsqrt(x)+x^2sqrt(x) ?

The derivative of xsqrt(x)+x^2sqrt(x) is (3sqrt(x)+5x^{3/2})/2

What is the first derivative of xsqrt(x)+x^2sqrt(x) ?

The first derivative of xsqrt(x)+x^2sqrt(x) is (3sqrt(x)+5x^{3/2})/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{3 x + 5 x ^{\frac{3}{2}}}{2}

Solution steps

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

Simplify

x x + x^{2} x : x^{\frac{3}{2}} + x^{\frac{5}{2}}

= \frac{d}{d x} (x^{\frac{3}{2}} + x^{\frac{5}{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{\frac{3}{2}}) + \frac{d}{d x} (x^{\frac{5}{2}})

\frac{d}{d x} (x^{\frac{3}{2}}) = \frac{3 x}{2}

\frac{d}{d x} (x^{\frac{5}{2}}) = \frac{5 x ^{\frac{3}{2}}}{2}

= \frac{3 x}{2} + \frac{5 x ^{\frac{3}{2}}}{2}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 x + 5 x ^{\frac{3}{2}}}{2}

\int (w^{2} + z^{2})^{\frac{- 1}{2}} w d w

4 e^{4 x} cos (5 x)

y^{^{''}} + 9 y = 2 sin (2 t), y (0) = 0, y^{^{'}} (0) = - 1

\frac{1}{1 - x - x ^{2}}, 0

n = 0 \sum \infty 4546644

What is the derivative of xsqrt(x)+x^2sqrt(x) ?
The derivative of xsqrt(x)+x^2sqrt(x) is (3sqrt(x)+5x^{3/2})/2
What is the first derivative of xsqrt(x)+x^2sqrt(x) ?
The first derivative of xsqrt(x)+x^2sqrt(x) is (3sqrt(x)+5x^{3/2})/2