What is the derivative of f(x)=(x^3+5)(x^3+x+1) ?

The derivative of f(x)=(x^3+5)(x^3+x+1) is 6x^5+4x^3+18x^2+5

What is the first derivative of f(x)=(x^3+5)(x^3+x+1) ?

The first derivative of f(x)=(x^3+5)(x^3+x+1) is 6x^5+4x^3+18x^2+5

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derivative of

f (x) = (x^{3} + 5) (x^{3} + x + 1)

6 x^{5} + 4 x^{3} + 18 x^{2} + 5

Solution steps

\frac{d}{d x} ((x^{3} + 5) (x^{3} + x + 1))

Apply the Product Rule:

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

f = x^{3} + 5, g = x^{3} + x + 1

= \frac{d}{d x} (x^{3} + 5) (x^{3} + x + 1) + \frac{d}{d x} (x^{3} + x + 1) (x^{3} + 5)

\frac{d}{d x} (x^{3} + 5) = 3 x^{2}

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

= 3 x^{2} (x^{3} + x + 1) + (3 x^{2} + 1) (x^{3} + 5)

Simplify

3 x^{2} (x^{3} + x + 1) + (3 x^{2} + 1) (x^{3} + 5) : 6 x^{5} + 4 x^{3} + 18 x^{2} + 5

= 6 x^{5} + 4 x^{3} + 18 x^{2} + 5

\int \frac{3}{x ln ( 2 x )} d x

\int 1 d x^{2}

y = 2 x + 6

\int \frac{20 x ^{3} - 40 x ^{2} + 7}{x ^{2} - 2 x} d x

f (x) = 3 e^{- x^{2}}

What is the derivative of f(x)=(x^3+5)(x^3+x+1) ?
The derivative of f(x)=(x^3+5)(x^3+x+1) is 6x^5+4x^3+18x^2+5
What is the first derivative of f(x)=(x^3+5)(x^3+x+1) ?
The first derivative of f(x)=(x^3+5)(x^3+x+1) is 6x^5+4x^3+18x^2+5