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Popular >

derivative of e^x(cos(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

(\partial)/(\partial y)(4x^2y^3+4)

\frac{\partial}{\partial y} (4 x^{2} y^{3} + 4)

d/(dt)(t^2sin(wt))

\frac{d}{d t} (t^{2} sin (wt))

integral of 1/((x^2+3)^{3/2)}

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

integral of 1/(sqrt(9x^2+36x+35))

\int \frac{1}{9 x ^{2} + 36 x + 35} d x

tangent of y=(8x)/(x^2-1),(3,3)tangent of

y = \frac{8 x}{x ^{2} - 1}, (3, 3)

Frequently Asked Questions (FAQ)

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