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Popular >

d/(d{y)}(sqrt({x)+{y}{z}})

Solution

\frac{d}{d y} (x + y z)

Solution

\frac{\frac{d}{d y} ( x ) + z}{2 x + y z}

Solution steps

\frac{d}{d y} (x + y z)

Apply the chain rule:

\frac{1}{2 x + y z} \frac{d}{d y} (x + y z)

= \frac{1}{2 x + y z} \frac{d}{d y} (x + y z)

\frac{d}{d y} (x + y z) = \frac{d}{d y} (x) + z

= \frac{1}{2 x + y z} (\frac{d}{d y} (x) + z)

Simplify

\frac{1}{2 x + y z} (\frac{d}{d y} (x) + z) : \frac{\frac{d}{d y} ( x ) + z}{2 x + y z}

= \frac{\frac{d}{d y} ( x ) + z}{2 x + y z}

Popular Examples

x*y^'=sqrt(1-y^2)

x \cdot y^{^{'}} = 1 - y^{2}

(\partial)/(\partial y)(arctan(xsqrt(y)))

\frac{\partial}{\partial y} (arctan (x y))

derivative of (ax+by(x)/(cx+dy))

\frac{d}{d x} (\frac{a x + b y ( x )}{c x + d y})

derivative of (e^x-1/(e^x+1))

\frac{d}{d x} (\frac{e ^{x} - 1}{e ^{x} + 1})

derivative of 1/((x^4+1^3))

\frac{d}{d x} (\frac{1}{( x ^{4} + 1 ) ^{3}})

Frequently Asked Questions (FAQ)

What is the d/(d{y)}(sqrt({x)+{y}{z}}) ?
The d/(d{y)}(sqrt({x)+{y}{z}}) is (d/(d{y)}({x})+{z}}{2sqrt({x)+{y)/z}}
What is the first d/(d{y)}(sqrt({x)+{y}{z}}) ?
The first d/(d{y)}(sqrt({x)+{y}{z}}) is (d/(d{y)}({x})+{z}}{2sqrt({x)+{y)/z}}