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Popular >

derivative of ax^2+by(x^2+c)

Solution

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

Solution

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))

Popular Examples

integral from 0 to y of integral from 0 to x of (x^2+y^2)^{3/2}

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

area 3x, 3/4 x,70-x^2 area

3 x, \frac{3}{4} x, 70 - x^{2}

q^{''}+20q^'+500q=12

q^{^{''}} + 20 q^{^{'}} + 500 q = 12

limit as x approaches 1 of 3x^2-2x+1

x \to 1 lim (3 x^{2} - 2 x + 1)

integral of cos^2(3x)sin^2(3x)

\int cos^{2} (3 x) sin^{2} (3 x) d x

Frequently Asked Questions (FAQ)

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))