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Popular >

derivative of e^ycos(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

derivative of y=x^2-7 derivative of

y = x^{2} - 7

integral of (8x^3)/((x^4+5))

\int \frac{8 x ^{3}}{( x ^{4} + 5 )} d x

integral of (x^3)/(x^2+x-6)

\int \frac{x ^{3}}{x ^{2} + x - 6} d x

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

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

area x^3,x^2 area

x^{3}, x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of e^ycos(x) ?
The derivative of e^ycos(x) is e^ycos(x)(dy)/(dx)-e^ysin(x)
What is the first derivative of e^ycos(x) ?
The first derivative of e^ycos(x) is e^ycos(x)(dy)/(dx)-e^ysin(x)