What is the derivative of y=(x+2)(x^2+1) ?

The derivative of y=(x+2)(x^2+1) is 3x^2+4x+1

What is the first derivative of y=(x+2)(x^2+1) ?

The first derivative of y=(x+2)(x^2+1) is 3x^2+4x+1

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derivative of

y = (x + 2) (x^{2} + 1)

3 x^{2} + 4 x + 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot (x^{2} + 1) + 2 x (x + 2)

Simplify

1 \cdot (x^{2} + 1) + 2 x (x + 2) : 3 x^{2} + 4 x + 1

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

h (x) = \frac{5}{6 x ^{5}}

(sin (x^{3} - 4 x + 2))^{^{'}}

(\frac{x + 1}{x}) + 5

\frac{- 2 x}{5}

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

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