What is the derivative of y=sqrt(x)(x^2+1)^3 ?

The derivative of y=sqrt(x)(x^2+1)^3 is ((x^2+1)^3)/(2sqrt(x))+6xsqrt(x)(x^2+1)^2

What is the first derivative of y=sqrt(x)(x^2+1)^3 ?

The first derivative of y=sqrt(x)(x^2+1)^3 is ((x^2+1)^3)/(2sqrt(x))+6xsqrt(x)(x^2+1)^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = x (x^{2} + 1)^{3}

\frac{( x ^{2} + 1 ) ^{3}}{2 x} + 6 x x (x^{2} + 1)^{2}

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x^{2} + 1)^{3}

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

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} ((x^{2} + 1)^{3}) = 6 x (x^{2} + 1)^{2}

= \frac{1}{2 x} (x^{2} + 1)^{3} + 6 x (x^{2} + 1)^{2} x

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

= \frac{( x ^{2} + 1 ) ^{3}}{2 x} + 6 x x (x^{2} + 1)^{2}

\int (cos (n x)) d x

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

n = 1 \sum \infty \frac{1}{3 ^{n}}

\int tan (5 θ) d θ

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

What is the derivative of y=sqrt(x)(x^2+1)^3 ?
The derivative of y=sqrt(x)(x^2+1)^3 is ((x^2+1)^3)/(2sqrt(x))+6xsqrt(x)(x^2+1)^2
What is the first derivative of y=sqrt(x)(x^2+1)^3 ?
The first derivative of y=sqrt(x)(x^2+1)^3 is ((x^2+1)^3)/(2sqrt(x))+6xsqrt(x)(x^2+1)^2