What is the derivative of Inx^3 ?

The derivative of Inx^3 is 3nIx^2

What is the first derivative of Inx^3 ?

The first derivative of Inx^3 is 3nIx^2

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\frac{d}{d x} (I n x^{3})

3 n I x^{2}

Solution steps

\frac{d}{d x} (I n x^{3})

Treat

n, I

as a constant

Take the constant out:

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

= I n \frac{d}{d x} (x^{3})

Apply the Power Rule:

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

= I n \cdot 3 x^{3 - 1}

Simplify

= 3 n I x^{2}

(4, - 9), (8, - 3)

\frac{d ^{2} x}{d t ^{2}} - 4 \frac{d x}{d t} = 4 x

\frac{d N}{d t} + N = Nt e^{t + 7}

\int_{- 1}^{0} (2 x - 1) d x

f^{^{''}} (x) = - f (x), f (0) = 0, f^{^{'}} (0) = 1