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Popular >

derivative of e^xsin(xcos(x))

Solution

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

Solution

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

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

Graph

Popular Examples

derivative of 1/x+1/y

\frac{d}{d x} (\frac{1}{x} + \frac{1}{y})

y^{''}+(y^')^2=0

y^{^{''}} + (y^{^{'}})^{2} = 0

area 7cos(7x),7-7cos(7x),[0, pi/7 ]area

7 cos (7 x), 7 - 7 cos (7 x), [0, \frac{π}{7}]

5ysqrt(x^2+1)(dy)/(dx)+4x=0

5 y x^{2} + 1 \frac{d y}{d x} + 4 x = 0

derivative of 1/((3x+1^2))

\frac{d}{d x} (\frac{1}{( 3 x + 1 ) ^{2}})

Frequently Asked Questions (FAQ)

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