en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=3x^2sin(x)

Solution

derivative of

y = 3 x^{2} sin (x)

Solution

3 (2 x sin (x) + cos (x) x^{2})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{2}, g = sin (x)

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

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

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

= 3 (2 x sin (x) + cos (x) x^{2})

Popular Examples

2y^{''}+3y^'-2y=25e^{-2t}

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 25 e^{- 2 t}

integral of 5/(9+4r^2)

\int \frac{5}{9 + 4 r ^{2}} d r

derivative of e^{kx}

\frac{d}{d x} (e^{k x})

integral from-5 to 5 of (sqrt(25-x^2))

\int_{- 5}^{5} (25 - x^{2}) d x

integral of 1/((4x+5)^{10)}

\int \frac{1}{( 4 x + 5 ) ^{10}} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=3x^2sin(x) ?
The derivative of y=3x^2sin(x) is 3(2xsin(x)+cos(x)x^2)
What is the first derivative of y=3x^2sin(x) ?
The first derivative of y=3x^2sin(x) is 3(2xsin(x)+cos(x)x^2)