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Popular >

derivative of 3x(x^3-1)

Solution

\frac{d}{d x} (3 x (x^{3} - 1))

Solution

3 (4 x^{3} - 1)

Solution steps

\frac{d}{d x} (3 x (x^{3} - 1))

Take the constant out:

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

= 3 \frac{d}{d x} (x (x^{3} - 1))

Apply the Product Rule:

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

f = x, g = x^{3} - 1

= 3 (\frac{d x}{d x} (x^{3} - 1) + \frac{d}{d x} (x^{3} - 1) x)

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

\frac{d}{d x} (x^{3} - 1) = 3 x^{2}

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

Simplify

3 (1 \cdot (x^{3} - 1) + 3 x^{2} x) : 3 (4 x^{3} - 1)

= 3 (4 x^{3} - 1)

Popular Examples

derivative of 1/((3x^2+x+2^5))

\frac{d}{d x} (\frac{1}{( 3 x ^{2} + x + 2 ) ^{5}})

integral of (-10)/((x-2)(x^2+4))

\int \frac{- 10}{( x - 2 ) ( x ^{2} + 4 )} d x

integral of (tan^4(x))/(sec^5(x))

\int \frac{tan ^{4} ( x )}{sec ^{5} ( x )} d x

y^{^{'}} = 4 y^{2} x

integral of 13tan^5(x)

\int 13 tan^{5} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of 3x(x^3-1) ?
The derivative of 3x(x^3-1) is 3(4x^3-1)
What is the first derivative of 3x(x^3-1) ?
The first derivative of 3x(x^3-1) is 3(4x^3-1)