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Popular Calculus >

derivative of f(x)=(1+2e^x)sin(x)

Solution

derivative of

f (x) = (1 + 2 e^{x}) sin (x)

Solution

2 e^{x} sin (x) + cos (x) (1 + 2 e^{x})

Solution steps

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

Apply the Product Rule:

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

f = 1 + 2 e^{x}, g = sin (x)

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

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

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

= 2 e^{x} sin (x) + cos (x) (1 + 2 e^{x})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(1+2e^x)sin(x) ?
The derivative of f(x)=(1+2e^x)sin(x) is 2e^xsin(x)+cos(x)(1+2e^x)
What is the first derivative of f(x)=(1+2e^x)sin(x) ?
The first derivative of f(x)=(1+2e^x)sin(x) is 2e^xsin(x)+cos(x)(1+2e^x)