What is the derivative of e^x(sin(x+cos(x))) ?

The derivative of e^x(sin(x+cos(x))) is 2e^xcos(x)

What is the first derivative of e^x(sin(x+cos(x))) ?

The first derivative of e^x(sin(x+cos(x))) is 2e^xcos(x)

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

2 e^{x} cos (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

e^{x} (sin (x) + cos (x)) + (cos (x) - sin (x)) e^{x} : 2 e^{x} cos (x)

= 2 e^{x} cos (x)

x^{3} - 2 x^{2} + 3 x + 5 (2)

\int_{e^{2}}^{e^{5}} (\frac{1}{x}) d x

(2, 5), (0, - 9)

\frac{u}{u ^{2} + 5}

\int e^{(- 0.1 x)} d x

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