What is the derivative of f(x)=(3x^2+2)(8x^3-3) ?

The derivative of f(x)=(3x^2+2)(8x^3-3) is 120x^4+48x^2-18x

What is the first derivative of f(x)=(3x^2+2)(8x^3-3) ?

The first derivative of f(x)=(3x^2+2)(8x^3-3) is 120x^4+48x^2-18x

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derivative of

f (x) = (3 x^{2} + 2) (8 x^{3} - 3)

120 x^{4} + 48 x^{2} - 18 x

Solution steps

\frac{d}{d x} ((3 x^{2} + 2) (8 x^{3} - 3))

Apply the Product Rule:

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

f = 3 x^{2} + 2, g = 8 x^{3} - 3

= \frac{d}{d x} (3 x^{2} + 2) (8 x^{3} - 3) + \frac{d}{d x} (8 x^{3} - 3) (3 x^{2} + 2)

\frac{d}{d x} (3 x^{2} + 2) = 6 x

\frac{d}{d x} (8 x^{3} - 3) = 24 x^{2}

= 6 x (8 x^{3} - 3) + 24 x^{2} (3 x^{2} + 2)

Simplify

6 x (8 x^{3} - 3) + 24 x^{2} (3 x^{2} + 2) : 120 x^{4} + 48 x^{2} - 18 x

= 120 x^{4} + 48 x^{2} - 18 x

\frac{d y}{d x} = 5 y x

\int \frac{30}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

\int 8 - x^{2} d x

x \to 1 lim (3 x^{2} + 3 x - 1)

What is the derivative of f(x)=(3x^2+2)(8x^3-3) ?
The derivative of f(x)=(3x^2+2)(8x^3-3) is 120x^4+48x^2-18x
What is the first derivative of f(x)=(3x^2+2)(8x^3-3) ?
The first derivative of f(x)=(3x^2+2)(8x^3-3) is 120x^4+48x^2-18x