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Popular >

derivative of 4x^3y^3

Solution

\frac{d}{d x} (4 x^{3} y^{3})

Solution

4 (3 x^{2} y^{3} + 3 y^{2} \frac{d y}{d x} x^{3})

Solution steps

\frac{d}{d x} (4 x^{3} y^{3})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{3} y^{3})

Apply the Product Rule:

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

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

= 4 (\frac{d}{d x} (x^{3}) y^{3} + \frac{d}{d x} (y^{3}) x^{3})

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

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

= 4 (3 x^{2} y^{3} + 3 y^{2} \frac{d y}{d x} x^{3})

Popular Examples

implicit (dy)/(dx),y^4=x implicit derivative

\frac{d y}{d x}, y^{4} = x

(\partial)/(\partial x)(-2cos(3x))

\frac{\partial}{\partial x} (- 2 cos (3 x))

integral from 0 to 1 of 1/(1+sqrt(x))

\int_{0}^{1} \frac{1}{1 + x} d x

sum from n=1 to infinity of n/(2n^4+2)

n = 1 \sum \infty \frac{n}{2 n ^{4} + 2}

integral from 0 to 1 of e^{3sqrt(x)}

\int_{0}^{1} e^{3 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 4x^3y^3 ?
The derivative of 4x^3y^3 is 4(3x^2y^3+3y^2(dy)/(dx)x^3)
What is the first derivative of 4x^3y^3 ?
The first derivative of 4x^3y^3 is 4(3x^2y^3+3y^2(dy)/(dx)x^3)