en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 7xsin(x)+x^2e^x

Solution

derivative of

7 x \cdot sin (x) + x^{2} \cdot e^{x}

Solution

7 (sin (x) + x cos (x)) + 2 x e^{x} + e^{x} x^{2}

Solution steps

\frac{d}{d x} (7 x sin (x) + x^{2} e^{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x sin (x)) + \frac{d}{d x} (x^{2} e^{x})

\frac{d}{d x} (7 x sin (x)) = 7 (sin (x) + x cos (x))

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

= 7 (sin (x) + x cos (x)) + 2 x e^{x} + e^{x} x^{2}

Graph

Popular Examples

derivative of 1/(3x^2-5/(2x))

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x})

x^2y^'-4xy=sin(2x)x^6

x^{2} y^{^{'}} - 4 x y = sin (2 x) x^{6}

derivative of sqrt(a+bx)

\frac{d}{d x} (a + b x)

derivative of (2xe^x/(x^2+1))

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

integral of 7x^2sin(2x)

\int 7 x^{2} sin (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of 7x*sin(x)+x^2*e^x ?
The derivative of 7x*sin(x)+x^2*e^x is 7(sin(x)+xcos(x))+2xe^x+e^xx^2
What is the first derivative of 7x*sin(x)+x^2*e^x ?
The first derivative of 7x*sin(x)+x^2*e^x is 7(sin(x)+xcos(x))+2xe^x+e^xx^2