What is the derivative of f(x)=(x^3+2)(x^5+7x^2+3) ?

The derivative of f(x)=(x^3+2)(x^5+7x^2+3) is 8x^7+45x^4+9x^2+28x

What is the first derivative of f(x)=(x^3+2)(x^5+7x^2+3) ?

The first derivative of f(x)=(x^3+2)(x^5+7x^2+3) is 8x^7+45x^4+9x^2+28x

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derivative of

f (x) = (x^{3} + 2) (x^{5} + 7 x^{2} + 3)

8 x^{7} + 45 x^{4} + 9 x^{2} + 28 x

Solution steps

\frac{d}{d x} ((x^{3} + 2) (x^{5} + 7 x^{2} + 3))

Apply the Product Rule:

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

f = x^{3} + 2, g = x^{5} + 7 x^{2} + 3

= \frac{d}{d x} (x^{3} + 2) (x^{5} + 7 x^{2} + 3) + \frac{d}{d x} (x^{5} + 7 x^{2} + 3) (x^{3} + 2)

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

\frac{d}{d x} (x^{5} + 7 x^{2} + 3) = 5 x^{4} + 14 x

= 3 x^{2} (x^{5} + 7 x^{2} + 3) + (5 x^{4} + 14 x) (x^{3} + 2)

Simplify

3 x^{2} (x^{5} + 7 x^{2} + 3) + (5 x^{4} + 14 x) (x^{3} + 2) : 8 x^{7} + 45 x^{4} + 9 x^{2} + 28 x

= 8 x^{7} + 45 x^{4} + 9 x^{2} + 28 x

\frac{d}{d x} (\frac{x + 2}{x ^{2} + 5 x + 6})

f (x) = 2 + 5 x

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

\frac{\partial}{\partial y} (- \frac{y}{x ^{2} + y ^{2}})

x \to 1 lim (lo g_{10} (x))

What is the derivative of f(x)=(x^3+2)(x^5+7x^2+3) ?
The derivative of f(x)=(x^3+2)(x^5+7x^2+3) is 8x^7+45x^4+9x^2+28x
What is the first derivative of f(x)=(x^3+2)(x^5+7x^2+3) ?
The first derivative of f(x)=(x^3+2)(x^5+7x^2+3) is 8x^7+45x^4+9x^2+28x