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Popular >

derivative of y=e^xsin(x)+cos(x)e^x

Solution

derivative of

y = e^{x} sin (x) + cos (x) e^{x}

Solution

2 e^{x} cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x} sin (x) + cos (x) e^{x} - e^{x} sin (x) + e^{x} cos (x)

Simplify

= 2 e^{x} cos (x)

Popular Examples

derivative of f(x)=((6x^2-6x+6)^5)derivative of

f (x) = ((6 x^{2} - 6 x + 6)^{5})

derivative of 3x^3ln(x^2)derivative of

3 x^{3} ln (x^{2})

sum from n=0 to infinity of 0

n = 0 \sum \infty 0

integral of sqrt(x)+x^2

\int x + x^{2} d x

tangent of y=5x^4+3x-6,(1,2)tangent of

y = 5 x^{4} + 3 x - 6, (1, 2)

Frequently Asked Questions (FAQ)

What is the derivative of y=e^xsin(x)+cos(x)e^x ?
The derivative of y=e^xsin(x)+cos(x)e^x is 2e^xcos(x)
What is the first derivative of y=e^xsin(x)+cos(x)e^x ?
The first derivative of y=e^xsin(x)+cos(x)e^x is 2e^xcos(x)