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Popular >

derivative of a+bx+cx^2+dx^3

Solution

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

Solution

3 d x^{2} + 2 c x + b

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

= 0 + b + 2 c x + 3 d x^{2}

Simplify

= 3 d x^{2} + 2 c x + b

Popular Examples

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(\partial)/(\partial x)(5xy^4)

\frac{\partial}{\partial x} (5 x y^{4})

(\partial)/(\partial y)(13/2 x^4y)

\frac{\partial}{\partial y} (\frac{13}{2} x^{4} y)

integral of (ln(sin(x)))/(sin^2(x))

\int \frac{ln ( sin ( x ) )}{sin ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of a+bx+cx^2+dx^3 ?
The derivative of a+bx+cx^2+dx^3 is 3dx^2+2cx+b
What is the first derivative of a+bx+cx^2+dx^3 ?
The first derivative of a+bx+cx^2+dx^3 is 3dx^2+2cx+b