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Popular >

derivative of x^3+3x^2+3x+1

Solution

\frac{d}{d x} (x^{3} + 3 x^{2} + 3 x + 1)

Solution

3 x^{2} + 6 x + 3

Solution steps

\frac{d}{d x} (x^{3} + 3 x^{2} + 3 x + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (3 x) + \frac{d}{d x} (1)

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

\frac{d}{d x} (3 x^{2}) = 6 x

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

\frac{d}{d x} (1) = 0

= 3 x^{2} + 6 x + 3 + 0

Simplify

= 3 x^{2} + 6 x + 3

Popular Examples

(\partial)/(\partial x)(3^{2x}+5^{4y}+2x+y^4)

\frac{\partial}{\partial x} (3^{2 x} + 5^{4 y} + 2 x + y^{4})

derivative of (x^3+x^2e^{2x})

\frac{d}{d x} ((x^{3} + x^{2}) e^{2 x})

integral of xsqrt(2)-1/(2sqrt(x))

\int x 2 - \frac{1}{2 x} d x

limit as x approaches 0 of (x+6)/(x^2+3)

x \to 0 lim (\frac{x + 6}{x ^{2} + 3})

integral of x^4sec^2(x^5+2)

\int x^{4} sec^{2} (x^{5} + 2) d x

Frequently Asked Questions (FAQ)

What is the derivative of x^3+3x^2+3x+1 ?
The derivative of x^3+3x^2+3x+1 is 3x^2+6x+3
What is the first derivative of x^3+3x^2+3x+1 ?
The first derivative of x^3+3x^2+3x+1 is 3x^2+6x+3