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

The derivative of f(x)=(5x^3+2)(3x^3+2) is 90x^5+48x^2

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

The first derivative of f(x)=(5x^3+2)(3x^3+2) is 90x^5+48x^2

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derivative of

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

90 x^{5} + 48 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (5 x^{3} + 2) = 15 x^{2}

\frac{d}{d x} (3 x^{3} + 2) = 9 x^{2}

= 15 x^{2} (3 x^{3} + 2) + 9 x^{2} (5 x^{3} + 2)

Simplify

15 x^{2} (3 x^{3} + 2) + 9 x^{2} (5 x^{3} + 2) : 90 x^{5} + 48 x^{2}

= 90 x^{5} + 48 x^{2}

n = 1 \sum \infty \frac{n - 1}{9 n - 1}

e^{- t} (t^{2} + 4 t + 5)

y^{^{'}} + 4 e^{x + y} = 0

x \to 0 lim (\frac{9 x ^{2} - 2 x}{x})

\frac{d}{d x} (arccos (- x))

What is the derivative of f(x)=(5x^3+2)(3x^3+2) ?
The derivative of f(x)=(5x^3+2)(3x^3+2) is 90x^5+48x^2
What is the first derivative of f(x)=(5x^3+2)(3x^3+2) ?
The first derivative of f(x)=(5x^3+2)(3x^3+2) is 90x^5+48x^2