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Popular >

derivative of e^{2x}sin(6x)

Solution

\frac{d}{d x} (e^{2 x} sin (6 x))

Solution

e^{2 x} \cdot 2 sin (6 x) + cos (6 x) \cdot 6 e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} sin (6 x))

Apply the Product Rule:

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

f = e^{2 x}, g = sin (6 x)

= \frac{d}{d x} (e^{2 x}) sin (6 x) + \frac{d}{d x} (sin (6 x)) e^{2 x}

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

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= e^{2 x} \cdot 2 sin (6 x) + cos (6 x) \cdot 6 e^{2 x}

Popular Examples

derivative of (4x-12/((x-2)^2))

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

derivative of-2.67+1.29x+6.28x^2+2.4x^3

\frac{d}{d x} (- 2.67 + 1.29 x + 6.28 x^{2} + 2.4 x^{3})

limit as x approaches 3-of sqrt(3-x)

x \to 3 - lim (3 - x)

integral of x^7sqrt(x^4+3)

\int x^{7} x^{4} + 3 d x

tangent of f(x)= 3/(x+1),(2,1)tangent of

f (x) = \frac{3}{x + 1}, (2, 1)

Frequently Asked Questions (FAQ)

What is the derivative of e^{2x}sin(6x) ?
The derivative of e^{2x}sin(6x) is e^{2x}*2sin(6x)+cos(6x)*6e^{2x}
What is the first derivative of e^{2x}sin(6x) ?
The first derivative of e^{2x}sin(6x) is e^{2x}*2sin(6x)+cos(6x)*6e^{2x}