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Popular >

derivative of e^x*sin(y)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

maclaurin x/((1+x^2)^2)maclaurin

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

f (x) = 2 x e^{x^{2}}

sum from n=0 to infinity}(1-10^{42 of)^n

n = 0 \sum \infty (1 - 1 0^{42})^{n}

derivative of ln(xsin(x))

\frac{d}{d x} (ln (x) sin (x))

(d^2y)/(dx^2)=3e^{-x},y(0)=1,y^'(0)=4

\frac{d ^{2} y}{d x ^{2}} = 3 e^{- x}, y (0) = 1, y^{^{'}} (0) = 4

Frequently Asked Questions (FAQ)

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