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

The derivative of 3x^2+xy+3y^2 is 6x+y

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

The first derivative of 3x^2+xy+3y^2 is 6x+y

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derivative of

3 x^{2} + x y + 3 y^{2}

6 x + y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (3 y^{2}) = 0

= 6 x + y + 0

Simplify

= 6 x + y

\frac{d}{d x} (\frac{x ^{2}}{100} + 8 + \frac{20}{x})

\frac{d}{d x} (cos (x) - 6 tan (x))

\frac{d}{d x} (\frac{3 x ^{2} + 9}{6 x})

f (x) = \frac{x + 1}{x ^{2} + 1}

e^{5 x}

What is the derivative of 3x^2+xy+3y^2 ?
The derivative of 3x^2+xy+3y^2 is 6x+y
What is the first derivative of 3x^2+xy+3y^2 ?
The first derivative of 3x^2+xy+3y^2 is 6x+y