What is the derivative of x^3+3xy^2-15x-12y ?

The derivative of x^3+3xy^2-15x-12y is 3x^2+3(y^2+2xy(dy)/(dx))-15-12(dy)/(dx)

What is the first derivative of x^3+3xy^2-15x-12y ?

The first derivative of x^3+3xy^2-15x-12y is 3x^2+3(y^2+2xy(dy)/(dx))-15-12(dy)/(dx)

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\frac{d}{d x} (x^{3} + 3 x y^{2} - 15 x - 12 y)

3 x^{2} + 3 (y^{2} + 2 x y \frac{d y}{d x}) - 15 - 12 \frac{d y}{d x}

Solution steps

\frac{d}{d x} (x^{3} + 3 x y^{2} - 15 x - 12 y)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (3 x y^{2}) - \frac{d}{d x} (15 x) - \frac{d}{d x} (12 y)

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

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

\frac{d}{d x} (15 x) = 15

\frac{d}{d x} (12 y) = 12 \frac{d y}{d x}

= 3 x^{2} + 3 (y^{2} + 2 x y \frac{d y}{d x}) - 15 - 12 \frac{d y}{d x}

\frac{d}{d x} (ln (9 x^{2} - 7 x + 1))

\frac{d y}{d t} = 5 - y

\frac{d}{d x} (e^{x} sin (3 x))

1500 x + 3000 (2 x + 3)^{- 1} - 1000

\int - ln (x) - \frac{ln ( x )}{16} d x

What is the derivative of x^3+3xy^2-15x-12y ?
The derivative of x^3+3xy^2-15x-12y is 3x^2+3(y^2+2xy(dy)/(dx))-15-12(dy)/(dx)
What is the first derivative of x^3+3xy^2-15x-12y ?
The first derivative of x^3+3xy^2-15x-12y is 3x^2+3(y^2+2xy(dy)/(dx))-15-12(dy)/(dx)