What is the derivative of (x^2+3)(x^3+5) ?

The derivative of (x^2+3)(x^3+5) is 5x^4+9x^2+10x

What is the first derivative of (x^2+3)(x^3+5) ?

The first derivative of (x^2+3)(x^3+5) is 5x^4+9x^2+10x

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derivative of

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

5 x^{4} + 9 x^{2} + 10 x

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + 3, g = x^{3} + 5

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

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

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

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

Simplify

2 x (x^{3} + 5) + 3 x^{2} (x^{2} + 3) : 5 x^{4} + 9 x^{2} + 10 x

= 5 x^{4} + 9 x^{2} + 10 x

x \to \infty lim (x^{3} e^{x})

f (x) = 2 x^{2} + 8 x, at x = 4

n \to 0 lim (sin (\frac{1}{n}))

\frac{d}{d x} (4 x^{2} cos (x) - x)

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

What is the derivative of (x^2+3)(x^3+5) ?
The derivative of (x^2+3)(x^3+5) is 5x^4+9x^2+10x
What is the first derivative of (x^2+3)(x^3+5) ?
The first derivative of (x^2+3)(x^3+5) is 5x^4+9x^2+10x