What is the derivative of x^2(1-xsqrt(x)) ?

The derivative of x^2(1-xsqrt(x)) is 2x(1-x^{3/2})-(3x^2sqrt(x))/2

What is the first derivative of x^2(1-xsqrt(x)) ?

The first derivative of x^2(1-xsqrt(x)) is 2x(1-x^{3/2})-(3x^2sqrt(x))/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^{2} (1 - x x))

2 x (1 - x^{\frac{3}{2}}) - \frac{3 x ^{2} x}{2}

Solution steps

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

Simplify

x^{2} (1 - x x) : x^{2} (1 - x^{\frac{3}{2}})

= \frac{d}{d x} (x^{2} (1 - x^{\frac{3}{2}}))

Apply the Product Rule:

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

f = x^{2}, g = 1 - x^{\frac{3}{2}}

= \frac{d}{d x} (x^{2}) (1 - x^{\frac{3}{2}}) + \frac{d}{d x} (1 - x^{\frac{3}{2}}) x^{2}

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

\frac{d}{d x} (1 - x^{\frac{3}{2}}) = - \frac{3 x}{2}

= 2 x (1 - x^{\frac{3}{2}}) + (- \frac{3 x}{2}) x^{2}

Simplify

2 x (1 - x^{\frac{3}{2}}) + (- \frac{3 x}{2}) x^{2} : 2 x (1 - x^{\frac{3}{2}}) - \frac{3 x ^{2} x}{2}

= 2 x (1 - x^{\frac{3}{2}}) - \frac{3 x ^{2} x}{2}

x \to \infty + lim (x^{2} e^{x})

\int sin^{2} (2 t) d t

\int_{0}^{5} x^{3} 1 + 9 x^{4} d x

\int \frac{4 x + 2}{e ^{x}} d x

\int \frac{1}{cos ^{2} ( t )} d t

What is the derivative of x^2(1-xsqrt(x)) ?
The derivative of x^2(1-xsqrt(x)) is 2x(1-x^{3/2})-(3x^2sqrt(x))/2
What is the first derivative of x^2(1-xsqrt(x)) ?
The first derivative of x^2(1-xsqrt(x)) is 2x(1-x^{3/2})-(3x^2sqrt(x))/2