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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (9 x y) = 9 (y + x \frac{d y}{d x})

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

Popular Examples

integral from-1 to 1 of (12-4x)^{-1}

\int_{- 1}^{1} (12 - 4 x)^{- 1} d x

integral of 6^x-sec^2(x)

\int 6^{x} - sec^{2} (x) d x

integral of 6x^2ln(x)

\int 6 x^{2} ln (x) d x

integral of 1/(9x^2-4)

\int \frac{1}{9 x ^{2} - 4} d x

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

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

Frequently Asked Questions (FAQ)

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