What is the derivative of (x^4+2x(x^3+2x^2+1)) ?

The derivative of (x^4+2x(x^3+2x^2+1)) is 7x^6+12x^5+12x^3+12x^2+2

What is the first derivative of (x^4+2x(x^3+2x^2+1)) ?

The first derivative of (x^4+2x(x^3+2x^2+1)) is 7x^6+12x^5+12x^3+12x^2+2

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\frac{d}{d x} ((x^{4} + 2 x) (x^{3} + 2 x^{2} + 1))

7 x^{6} + 12 x^{5} + 12 x^{3} + 12 x^{2} + 2

Solution steps

\frac{d}{d x} ((x^{4} + 2 x) (x^{3} + 2 x^{2} + 1))

Apply the Product Rule:

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

f = x^{4} + 2 x, g = x^{3} + 2 x^{2} + 1

= \frac{d}{d x} (x^{4} + 2 x) (x^{3} + 2 x^{2} + 1) + \frac{d}{d x} (x^{3} + 2 x^{2} + 1) (x^{4} + 2 x)

\frac{d}{d x} (x^{4} + 2 x) = 4 x^{3} + 2

\frac{d}{d x} (x^{3} + 2 x^{2} + 1) = 3 x^{2} + 4 x

= (4 x^{3} + 2) (x^{3} + 2 x^{2} + 1) + (3 x^{2} + 4 x) (x^{4} + 2 x)

Simplify

(4 x^{3} + 2) (x^{3} + 2 x^{2} + 1) + (3 x^{2} + 4 x) (x^{4} + 2 x) : 7 x^{6} + 12 x^{5} + 12 x^{3} + 12 x^{2} + 2

= 7 x^{6} + 12 x^{5} + 12 x^{3} + 12 x^{2} + 2

\frac{d}{d x} (\frac{ln ( x )}{1 + ln ( x )})

y^{^{'}} = arctan (\frac{x}{2})

\int x \cdot e^{- 5 x} d x

\frac{d}{d x} (5^{5 x})

\int \frac{1}{3} tan (3 x) d x

What is the derivative of (x^4+2x(x^3+2x^2+1)) ?
The derivative of (x^4+2x(x^3+2x^2+1)) is 7x^6+12x^5+12x^3+12x^2+2
What is the first derivative of (x^4+2x(x^3+2x^2+1)) ?
The first derivative of (x^4+2x(x^3+2x^2+1)) is 7x^6+12x^5+12x^3+12x^2+2