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Popular >

derivative of 3x^3y^2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{3}, g = y^{2}

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

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

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

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

Popular Examples

(dy)/(dx)=(2x+sec^2(x))/(4y)

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{4 y}

(\partial)/(\partial y)(yln(x))

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

derivative of 40x^4+180x^3+240x^2+100x

\frac{d}{d x} (40 x^{4} + 180 x^{3} + 240 x^{2} + 100 x)

derivative of 1/3 (3-5x^3)

\frac{d}{d x} (\frac{1}{3} (3 - 5 x)^{3})

integral from 0 to 2 of (16)/(21x^2)

\int_{0}^{2} \frac{16}{21 x ^{2}} d x

Frequently Asked Questions (FAQ)

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