What is the derivative of ax^2+by(x^2+c) ?

The derivative of ax^2+by(x^2+c) is 2ax+b(x^2 derivative of {y}(x)+2x{y}(x))

What is the first derivative of ax^2+by(x^2+c) ?

The first derivative of ax^2+by(x^2+c) is 2ax+b(x^2 derivative of {y}(x)+2x{y}(x))

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d c}{d x} = 0

= 2 a x + b (\frac{d}{d x} (y (x)) x^{2} + 2 x y (x)) + 0

Simplify

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

What is the derivative of ax^2+by(x^2+c) ?
The derivative of ax^2+by(x^2+c) is 2ax+b(x^2 derivative of {y}(x)+2x{y}(x))
What is the first derivative of ax^2+by(x^2+c) ?
The first derivative of ax^2+by(x^2+c) is 2ax+b(x^2 derivative of {y}(x)+2x{y}(x))