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Popular >

derivative of 6x^2+15xy+3y^2

Solution

\frac{d}{d x} (6 x^{2} + 15 x y + 3 y^{2})

Solution

12 x + 15 (y + x \frac{d y}{d x}) + 6 y \frac{d y}{d x}

Solution steps

\frac{d}{d x} (6 x^{2} + 15 x y + 3 y^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (15 x y) + \frac{d}{d x} (3 y^{2})

\frac{d}{d x} (6 x^{2}) = 12 x

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

\frac{d}{d x} (3 y^{2}) = 6 y \frac{d y}{d x}

= 12 x + 15 (y + x \frac{d y}{d x}) + 6 y \frac{d y}{d x}

Popular Examples

integral of (e^xx)

\int (e^{x} x) d x

limit as x approaches infinity of ((e^{2x}-8-19x))/((19x)^2)

x \to \infty lim (\frac{( e ^{2 x} - 8 - 19 x )}{( 19 x ) ^{2}})

y^{^{''}} + 49 y = 0

integral of 64sin^2(x)

\int 64 sin^{2} (x) d x

tangent of f(x)=x^3-11x,\at x=3 tangent of

f (x) = x^{3} - 11 x, at x = 3

Frequently Asked Questions (FAQ)

What is the derivative of 6x^2+15xy+3y^2 ?
The derivative of 6x^2+15xy+3y^2 is 12x+15(y+x(dy)/(dx))+6y(dy)/(dx)
What is the first derivative of 6x^2+15xy+3y^2 ?
The first derivative of 6x^2+15xy+3y^2 is 12x+15(y+x(dy)/(dx))+6y(dy)/(dx)