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Popular >

derivative of 3xsqrt(y)

Solution

\frac{d}{d x} (3 x y)

Solution

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

Solution steps

\frac{d}{d x} (3 x y)

Take the constant out:

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

= 3 \frac{d}{d x} (x y)

Apply the Product Rule:

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

f = x, g = y

= 3 (\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}

= 3 (1 \cdot y + \frac{\frac{d y}{d x}}{2 y} x)

Simplify

3 (1 \cdot y + \frac{\frac{d y}{d x}}{2 y} x) : 3 (y + \frac{x \frac{d y}{d x}}{2 y})

= 3 (y + \frac{x \frac{d y}{d x}}{2 y})

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\frac{d}{d x} (ln (arctan (8 x^{5})))

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

integral of \sqrt[3]{x}*(x+1)^2

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

(1+y^2+xy^2)dx+(x^2y+y+2xy)dy=0

(1 + y^{2} + x y^{2}) d x + (x^{2} y + y + 2 x y) d y = 0

Frequently Asked Questions (FAQ)

What is the derivative of 3xsqrt(y) ?
The derivative of 3xsqrt(y) is 3(sqrt(y)+(x\frac{dy)/(dx)}{2sqrt(y)})
What is the first derivative of 3xsqrt(y) ?
The first derivative of 3xsqrt(y) is 3(sqrt(y)+(x\frac{dy)/(dx)}{2sqrt(y)})