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Popular >

d/(d{y)}({x}e^{({y})/({z)}})

Solution

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

Solution

\frac{e ^{\frac{y}{z}} x}{z}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

e^{\frac{y}{z}} \frac{d}{d y} (\frac{y}{z})

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

\frac{d}{d y} (\frac{y}{z}) = \frac{1}{z}

= x e^{\frac{y}{z}} \frac{1}{z}

Simplify

x e^{\frac{y}{z}} \frac{1}{z} : \frac{e ^{\frac{y}{z}} x}{z}

= \frac{e ^{\frac{y}{z}} x}{z}

Popular Examples

integral of ((arctan(x))^3)/(x^2+1)

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

derivative of 2sin(2cos(x))

\frac{d}{d x} (2 sin (2 cos (x)))

derivative of 1/(sqrt(1+4x^2+x^4))

\frac{d}{d x} (\frac{1}{1 + 4 x ^{2} + x ^{4}})

integral of 2x^6-3x^5+11x^2+1

\int 2 x^{6} - 3 x^{5} + 11 x^{2} + 1 d x

integral of (-gt+V)

\int (- g t + V) d t

Frequently Asked Questions (FAQ)

What is the d/(d{y)}({x}e^{({y})/({z)}}) ?
The d/(d{y)}({x}e^{({y})/({z)}}) is (e^{({y})/({z)})/x}{{z}}
What is the first d/(d{y)}({x}e^{({y})/({z)}}) ?
The first d/(d{y)}({x}e^{({y})/({z)}}) is (e^{({y})/({z)})/x}{{z}}