en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y^2(x^2+1)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = y^{2}, g = x^{2} + 1

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

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

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

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

Popular Examples

integral of (esqrt(3x+1))/(sqrt(3x+1))

\int \frac{e 3 x + 1}{3 x + 1} d x

derivative of-6x^2+3200x-61600

\frac{d}{d x} (- 6 x^{2} + 3200 x - 61600)

(\partial)/(\partial x)(x/(2y+x))

\frac{\partial}{\partial x} (\frac{x}{2 y + x})

derivative of 2sqrt(y)derivative of

2 y

integral from 1 to 2 of (4ln(x))/(x^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of y^2(x^2+1) ?
The derivative of y^2(x^2+1) is 2y(dy)/(dx)(x^2+1)+2xy^2
What is the first derivative of y^2(x^2+1) ?
The first derivative of y^2(x^2+1) is 2y(dy)/(dx)(x^2+1)+2xy^2