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Popular >

derivative of 3x(8x^3-2)

Solution

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

Solution

3 (32 x^{3} - 2)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 3 (1 \cdot (8 x^{3} - 2) + 24 x^{2} x)

Simplify

3 (1 \cdot (8 x^{3} - 2) + 24 x^{2} x) : 3 (32 x^{3} - 2)

= 3 (32 x^{3} - 2)

Popular Examples

derivative of e^{2ln(x})

\frac{d}{d x} (e^{2 l n (x)})

(dx)/(dt)+4t^3x^5+x/t =0

\frac{d x}{d t} + 4 t^{3} x^{5} + \frac{x}{t} = 0

derivative of (x-1/x ^4)

\frac{d}{d x} ((x - \frac{1}{x})^{4})

limit as x approaches 5 of-x^2+8x-5

x \to 5 lim (- x^{2} + 8 x - 5)

integral from 0 to 4 of (e^x)^2

\int_{0}^{4} (e^{x})^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of 3x(8x^3-2) ?
The derivative of 3x(8x^3-2) is 3(32x^3-2)
What is the first derivative of 3x(8x^3-2) ?
The first derivative of 3x(8x^3-2) is 3(32x^3-2)