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Popular >

derivative of (y(x^3+ax^2+bx+c))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = x^{3} + a x^{2} + b x + c

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

\frac{d}{d x} (x^{3} + a x^{2} + b x + c) = 3 x^{2} + 2 a x + b

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

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Frequently Asked Questions (FAQ)

What is the derivative of (y(x^3+ax^2+bx+c)) ?
The derivative of (y(x^3+ax^2+bx+c)) is (dy)/(dx)(x^3+ax^2+bx+c)+(3x^2+2ax+b)y
What is the first derivative of (y(x^3+ax^2+bx+c)) ?
The first derivative of (y(x^3+ax^2+bx+c)) is (dy)/(dx)(x^3+ax^2+bx+c)+(3x^2+2ax+b)y