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Popular >

derivative of 9x^3-4y^2+2xy

Solution

\frac{d}{d x} (9 x^{3} - 4 y^{2} + 2 x y)

Solution

27 x^{2} - 8 y \frac{d y}{d x} + 2 (y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (9 x^{3} - 4 y^{2} + 2 x y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (9 x^{3}) - \frac{d}{d x} (4 y^{2}) + \frac{d}{d x} (2 x y)

\frac{d}{d x} (9 x^{3}) = 27 x^{2}

\frac{d}{d x} (4 y^{2}) = 8 y \frac{d y}{d x}

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

= 27 x^{2} - 8 y \frac{d y}{d x} + 2 (y + x \frac{d y}{d x})

Popular Examples

(\partial)/(\partial x)(-y^2x)

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

integral of 10^x

\int 1 0^{x} d x

(\partial)/(\partial x)(2x^2-x^2y^3+y^2)

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

integral from-1 to 1 of (e^x)/(e^x-1)

\int_{- 1}^{1} \frac{e ^{x}}{e ^{x} - 1} d x

derivative of ln((2x+3/(2x-3)))

\frac{d}{d x} (ln (\frac{2 x + 3}{2 x - 3}))

Frequently Asked Questions (FAQ)

What is the derivative of 9x^3-4y^2+2xy ?
The derivative of 9x^3-4y^2+2xy is 27x^2-8y(dy)/(dx)+2(y+x(dy)/(dx))
What is the first derivative of 9x^3-4y^2+2xy ?
The first derivative of 9x^3-4y^2+2xy is 27x^2-8y(dy)/(dx)+2(y+x(dy)/(dx))