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Popular >

derivative of 3xy^2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = y^{2}

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

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

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

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

Simplify

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

Popular Examples

derivative of (sin(y)/(sin(x)))

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

derivative of y(θ)= pi/8 sin(θ)derivative of

y (θ) = \frac{π}{8} sin (θ)

integral of 1/(b^2sqrt(25+b^2))

\int \frac{1}{b ^{2} 25 + b ^{2}} d b

derivative of 2-4cos(x)

\frac{d}{d x} (2 - 4 cos (x))

y^'=(xy)/(1-x^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of 3xy^2 ?
The derivative of 3xy^2 is 3(y^2+2xy(dy)/(dx))
What is the first derivative of 3xy^2 ?
The first derivative of 3xy^2 is 3(y^2+2xy(dy)/(dx))