What is the derivative of 5sqrt((xy/2)) ?

The derivative of 5sqrt((xy/2)) is (5(y+x\frac{dy)/(dx))}{2sqrt(2)sqrt(xy)}

What is the first derivative of 5sqrt((xy/2)) ?

The first derivative of 5sqrt((xy/2)) is (5(y+x\frac{dy)/(dx))}{2sqrt(2)sqrt(xy)}

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\frac{d}{d x} (5 \frac{x y}{2})

\frac{5 ( y + x \frac{d y}{d x} )}{2 2 x y}

Solution steps

\frac{d}{d x} (5 \frac{x y}{2})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{x y}{2})

Apply the chain rule:

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

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

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

= 5 \cdot \frac{1}{2 \frac{x y}{2}} \cdot \frac{1}{2} (y + x \frac{d y}{d x})

Simplify

5 \cdot \frac{1}{2 \frac{x y}{2}} \cdot \frac{1}{2} (y + x \frac{d y}{d x}) : \frac{5 ( y + x \frac{d y}{d x} )}{2 2 x y}

= \frac{5 ( y + x \frac{d y}{d x} )}{2 2 x y}

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

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

4 x^{3} + e^{16 x} - 3^{2 x - 1}

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

What is the derivative of 5sqrt((xy/2)) ?
The derivative of 5sqrt((xy/2)) is (5(y+x\frac{dy)/(dx))}{2sqrt(2)sqrt(xy)}
What is the first derivative of 5sqrt((xy/2)) ?
The first derivative of 5sqrt((xy/2)) is (5(y+x\frac{dy)/(dx))}{2sqrt(2)sqrt(xy)}