What is the derivative of ((x^2-1^3)/4) ?

The derivative of ((x^2-1^3)/4) is (3x(x^2-1)^2)/2

What is the first derivative of ((x^2-1^3)/4) ?

The first derivative of ((x^2-1^3)/4) is (3x(x^2-1)^2)/2

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\frac{d}{d x} (\frac{( x ^{2} - 1 ) ^{3}}{4})

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

Solution steps

\frac{d}{d x} (\frac{( x ^{2} - 1 ) ^{3}}{4})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} ((x^{2} - 1)^{3})

Apply the chain rule:

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

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

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

= \frac{1}{4} \cdot 3 (x^{2} - 1)^{2} \cdot 2 x

Simplify

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

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

n = 0 \sum \infty \frac{e ^{n}}{n ^{n}}

\frac{\partial}{\partial y} (sin (x^{2}) - y)

\frac{d}{d x} (2 sin (x))

arcsin (\frac{2}{3})

y^{^{'}} + 6 x^{5} y = x^{5}

What is the derivative of ((x^2-1^3)/4) ?
The derivative of ((x^2-1^3)/4) is (3x(x^2-1)^2)/2
What is the first derivative of ((x^2-1^3)/4) ?
The first derivative of ((x^2-1^3)/4) is (3x(x^2-1)^2)/2