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Popular >

derivative of e^xcos(8x)

Solution

\frac{d}{d x} (e^{x} cos (8 x))

Solution

e^{x} cos (8 x) - 8 e^{x} sin (8 x)

Solution steps

\frac{d}{d x} (e^{x} cos (8 x))

Apply the Product Rule:

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

f = e^{x}, g = cos (8 x)

= \frac{d}{d x} (e^{x}) cos (8 x) + \frac{d}{d x} (cos (8 x)) e^{x}

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

\frac{d}{d x} (cos (8 x)) = - sin (8 x) \cdot 8

= e^{x} cos (8 x) + (- sin (8 x) \cdot 8) e^{x}

Simplify

= e^{x} cos (8 x) - 8 e^{x} sin (8 x)

Popular Examples

tangent of f(x)= x/(x-3),\at x=1 tangent of

f (x) = \frac{x}{x - 3}, at x = 1

(\partial)/(\partial x)(3x^2+xy+y^2-8)

\frac{\partial}{\partial x} (3 x^{2} + x y + y^{2} - 8)

(\partial)/(\partial x)(6/(x-2)+7x)

\frac{\partial}{\partial x} (\frac{6}{x - 2} + 7 x)

integral of (x^2-5x+2)

\int (x^{2} - 5 x + 2) d x

derivative of log_{e}(3x)

\frac{d}{d x} (lo g_{e} (3 x))

Frequently Asked Questions (FAQ)

What is the derivative of e^xcos(8x) ?
The derivative of e^xcos(8x) is e^xcos(8x)-8e^xsin(8x)
What is the first derivative of e^xcos(8x) ?
The first derivative of e^xcos(8x) is e^xcos(8x)-8e^xsin(8x)