en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=x^2sin(pix)

Solution

derivative of

y = x^{2} sin (π x)

Solution

2 x sin (π x) + cos (π x) π x^{2}

Solution steps

\frac{d}{d x} (x^{2} sin (π x))

Apply the Product Rule:

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

f = x^{2}, g = sin (π x)

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

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

\frac{d}{d x} (sin (π x)) = cos (π x) π

= 2 x sin (π x) + cos (π x) π x^{2}

Graph

Popular Examples

(\partial)/(\partial x)(-5x^2-2xy-3y^2)

\frac{\partial}{\partial x} (- 5 x^{2} - 2 x y - 3 y^{2})

derivative of arccot(x/9)derivative of

arccot (\frac{x}{9})

integral of (sqrt(x)-1)/(sqrt(x)+1)

\int \frac{x - 1}{x + 1} d x

integral of (2x+3)/((x+1)^2)

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

implicit 8x^2+7y^2=56 implicit derivative

8 x^{2} + 7 y^{2} = 56

Frequently Asked Questions (FAQ)

What is the derivative of y=x^2sin(pix) ?
The derivative of y=x^2sin(pix) is 2xsin(pix)+cos(pix)pix^2
What is the first derivative of y=x^2sin(pix) ?
The first derivative of y=x^2sin(pix) is 2xsin(pix)+cos(pix)pix^2