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Popular >

derivative of x(2x-y^3)

Solution

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

Solution

4 x - 3 x y^{2} \frac{d y}{d x} - y^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (2 x - y^{3}) + (2 - 3 y^{2} \frac{d y}{d x}) x : 4 x - 3 x y^{2} \frac{d y}{d x} - y^{3}

= 4 x - 3 x y^{2} \frac{d y}{d x} - y^{3}

Popular Examples

(d^2)/(dx^2)((x^2+10)^6)

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 10)^{6})

sum from n=1 to infinity of 1/(3^n+1)

n = 1 \sum \infty \frac{1}{3 ^{n} + 1}

derivative of 2x-3x^2

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

(\partial)/(\partial y)(-2xy-y^4)

\frac{\partial}{\partial y} (- 2 x y - y^{4})

limit as x approaches 0 of (x-sin(x)}{e^x-1-x-\frac{x^2)/2}

x \to 0 lim (\frac{x - sin ( x )}{e ^{x} - 1 - x - \frac{x ^{2}}{2}})

Frequently Asked Questions (FAQ)

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