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Popular >

derivative of e^x(sin(x-cos(x)))

Solution

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

Solution

2 e^{x} sin (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} sin (x)

= 2 e^{x} sin (x)

Popular Examples

area x^2,12-x,-4,3 area

x^{2}, 12 - x, - 4, 3

integral of (-x^4+1)^2(-4x^3)

\int (- x^{4} + 1)^{2} (- 4 x^{3}) d x

integral of 1/(x^2-2)

\int \frac{1}{x ^{2} - 2} d x

limit as x approaches 3 of 1/(1+(\frac{1){x-3})}

x \to 3 lim (\frac{1}{1 + ( \frac{1}{x - 3} )})

derivative of (8x^3-6/(x^2))

\frac{d}{d x} (\frac{8 x ^{3} - 6}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of e^x(sin(x-cos(x))) ?
The derivative of e^x(sin(x-cos(x))) is 2e^xsin(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^xsin(x)