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Popular >

derivative of e^{3x}sin(x^2)

Solution

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

Solution

e^{3 x} \cdot 3 sin (x^{2}) + cos (x^{2}) \cdot 2 x e^{3 x}

Solution steps

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

Apply the Product Rule:

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

f = e^{3 x}, g = sin (x^{2})

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

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

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

Popular Examples

area 7x^2,x^2+3 area

7 x^{2}, x^{2} + 3

limit as x approaches 3 of (x^2-9)/(3-x)

x \to 3 lim (\frac{x ^{2} - 9}{3 - x})

y^{''}-8y^'+16y=0

y^{^{''}} - 8 y^{^{'}} + 16 y = 0

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

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

derivative of (sin(x)/(cos(x^2)))

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

Frequently Asked Questions (FAQ)

What is the derivative of e^{3x}sin(x^2) ?
The derivative of e^{3x}sin(x^2) is e^{3x}*3sin(x^2)+cos(x^2)*2xe^{3x}
What is the first derivative of e^{3x}sin(x^2) ?
The first derivative of e^{3x}sin(x^2) is e^{3x}*3sin(x^2)+cos(x^2)*2xe^{3x}