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Popular >

derivative of xsqrt(y)

Solution

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

Solution

y + \frac{x \frac{d y}{d x}}{2 y}

Solution steps

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

Apply the Product Rule:

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

f = x, g = y

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

\frac{d x}{d x} = 1

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

= 1 \cdot y + \frac{\frac{d y}{d x}}{2 y} x

Simplify

1 \cdot y + \frac{\frac{d y}{d x}}{2 y} x : y + \frac{x \frac{d y}{d x}}{2 y}

= y + \frac{x \frac{d y}{d x}}{2 y}

Popular Examples

y^{''}+2y^'+2y=e^{-t}sin(t)

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- t} sin (t)

f^'(x)=((1-sec(x))/(tan(x)))

f^{^{'}} (x) = (\frac{1 - sec ( x )}{tan ( x )})

(\partial)/(\partial x)(1-x^2)

\frac{\partial}{\partial x} (1 - x^{2})

(\partial)/(\partial x)(rcos(t)sin(x))

\frac{\partial}{\partial x} (r cos (t) sin (x))

integral of x/((x+3))

\int \frac{x}{( x + 3 )} d x

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(y) ?
The derivative of xsqrt(y) is sqrt(y)+(x\frac{dy)/(dx)}{2sqrt(y)}
What is the first derivative of xsqrt(y) ?
The first derivative of xsqrt(y) is sqrt(y)+(x\frac{dy)/(dx)}{2sqrt(y)}