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Popular >

derivative of e^x*cos(y)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral of ye^y

\int y e^{y} d y

limit as x approaches infinity of 5x+4

x \to \infty lim (5 x + 4)

(\partial)/(\partial x)(xsin(7x^2y))

\frac{\partial}{\partial x} (x sin (7 x^{2} y))

limit as x approaches 0 of (x^2+1)/x

x \to 0 lim (\frac{x ^{2} + 1}{x})

derivative of G(t)=(1-5t)/(4+t)derivative of

G (t) = \frac{1 - 5 t}{4 + t}

Frequently Asked Questions (FAQ)

What is the derivative of e^x*cos(y) ?
The derivative of e^x*cos(y) is e^xcos(y)-e^xsin(y)(dy)/(dx)
What is the first derivative of e^x*cos(y) ?
The first derivative of e^x*cos(y) is e^xcos(y)-e^xsin(y)(dy)/(dx)