What is (\partial)/(\partial x)(ax^2+by^2) ?

The answer to (\partial)/(\partial x)(ax^2+by^2) is 2ax

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(\partial)/(\partial x)(ax^2+by^2)

\frac{\partial}{\partial x} (a x^{2} + b y^{2})

2 a x

Solution steps

\frac{\partial}{\partial x} (a x^{2} + b y^{2})

Treat

a, b, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (a x^{2}) + \frac{\partial}{\partial x} (b y^{2})

\frac{\partial}{\partial x} (a x^{2}) = 2 a x

\frac{\partial}{\partial x} (b y^{2}) = 0

= 2 a x + 0

Simplify

= 2 a x

\frac{d}{d x} (\frac{x}{x ^{2} + 81})

f (x) = 3 x + \frac{8}{x ^{3}}

n = 0 \sum \infty n + (- 1)^{n}

\frac{e ^{x} + e ^{- x}}{e ^{2 x}}

(2 x^{4})^{^{'}}

What is (\partial)/(\partial x)(ax^2+by^2) ?
The answer to (\partial)/(\partial x)(ax^2+by^2) is 2ax