What is the derivative of f(x)=(8x+9)(x^3-6) ?

The derivative of f(x)=(8x+9)(x^3-6) is 32x^3+27x^2-48

What is the first derivative of f(x)=(8x+9)(x^3-6) ?

The first derivative of f(x)=(8x+9)(x^3-6) is 32x^3+27x^2-48

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derivative of

f (x) = (8 x + 9) (x^{3} - 6)

32 x^{3} + 27 x^{2} - 48

Solution steps

\frac{d}{d x} ((8 x + 9) (x^{3} - 6))

Apply the Product Rule:

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

f = 8 x + 9, g = x^{3} - 6

= \frac{d}{d x} (8 x + 9) (x^{3} - 6) + \frac{d}{d x} (x^{3} - 6) (8 x + 9)

\frac{d}{d x} (8 x + 9) = 8

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

= 8 (x^{3} - 6) + 3 x^{2} (8 x + 9)

Simplify

8 (x^{3} - 6) + 3 x^{2} (8 x + 9) : 32 x^{3} + 27 x^{2} - 48

= 32 x^{3} + 27 x^{2} - 48

- 64 cos (2 x)

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\frac{d}{d x} (1 - sec (x))

\int (x^{1.5} + 9 x^{3.5}) d x

(7 x + 2 y) \frac{d y}{d x} = - 2 x - 7 y

What is the derivative of f(x)=(8x+9)(x^3-6) ?
The derivative of f(x)=(8x+9)(x^3-6) is 32x^3+27x^2-48
What is the first derivative of f(x)=(8x+9)(x^3-6) ?
The first derivative of f(x)=(8x+9)(x^3-6) is 32x^3+27x^2-48