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Popular >

derivative of e^{x^2}sin(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

(dx)/(dt)=2x(10-x)

\frac{d x}{d t} = 2 x (10 - x)

(\partial)/(\partial t)(e^tsin(t))

\frac{\partial}{\partial t} (e^{t} sin (t))

derivative of 3ln(4x)

\frac{d}{d x} (3 ln (4 x))

integral from 1 to 3 of (4x-3)^2-(x^2)^2

\int_{1}^{3} (4 x - 3)^{2} - (x^{2})^{2} d x

integral of (6x^2+8)/(x^3+4x)

\int \frac{6 x ^{2} + 8}{x ^{3} + 4 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of e^{x^2}sin(x) ?
The derivative of e^{x^2}sin(x) is e^{x^2}*2xsin(x)+cos(x)e^{x^2}
What is the first derivative of e^{x^2}sin(x) ?
The first derivative of e^{x^2}sin(x) is e^{x^2}*2xsin(x)+cos(x)e^{x^2}