What is the derivative of 24x(3x^2-1)^3 ?

The derivative of 24x(3x^2-1)^3 is 24((3x^2-1)^3+18x^2(3x^2-1)^2)

What is the first derivative of 24x(3x^2-1)^3 ?

The first derivative of 24x(3x^2-1)^3 is 24((3x^2-1)^3+18x^2(3x^2-1)^2)

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derivative of

24 x (3 x^{2} - 1)^{3}

24 ((3 x^{2} - 1)^{3} + 18 x^{2} (3 x^{2} - 1)^{2})

Solution steps

\frac{d}{d x} (24 x (3 x^{2} - 1)^{3})

Take the constant out:

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

= 24 \frac{d}{d x} (x (3 x^{2} - 1)^{3})

Apply the Product Rule:

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

f = x, g = (3 x^{2} - 1)^{3}

= 24 (\frac{d x}{d x} (3 x^{2} - 1)^{3} + \frac{d}{d x} ((3 x^{2} - 1)^{3}) x)

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

\frac{d}{d x} ((3 x^{2} - 1)^{3}) = 18 x (3 x^{2} - 1)^{2}

= 24 (1 \cdot (3 x^{2} - 1)^{3} + 18 x (3 x^{2} - 1)^{2} x)

Simplify

24 (1 \cdot (3 x^{2} - 1)^{3} + 18 x (3 x^{2} - 1)^{2} x) : 24 ((3 x^{2} - 1)^{3} + 18 x^{2} (3 x^{2} - 1)^{2})

= 24 ((3 x^{2} - 1)^{3} + 18 x^{2} (3 x^{2} - 1)^{2})

x^{2} \cdot \frac{d y}{d x} = y - x y

\int (x^{2} y) d y

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

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 14, y^{^{'}} (0) = b

\frac{d}{d x} (\frac{2 x ^{5} - 3 x ^{4} - 7 x ^{3}}{x ^{4}})

What is the derivative of 24x(3x^2-1)^3 ?
The derivative of 24x(3x^2-1)^3 is 24((3x^2-1)^3+18x^2(3x^2-1)^2)
What is the first derivative of 24x(3x^2-1)^3 ?
The first derivative of 24x(3x^2-1)^3 is 24((3x^2-1)^3+18x^2(3x^2-1)^2)