What is the derivative of (x+h^3) ?

The derivative of (x+h^3) is 3(x+h)^2

What is the first derivative of (x+h^3) ?

The first derivative of (x+h^3) is 3(x+h)^2

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\frac{d}{d x} ((x + h)^{3})

3 (x + h)^{2}

Solution steps

\frac{d}{d x} ((x + h)^{3})

Treat

h

as a constant

Apply the chain rule:

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

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

\frac{d}{d x} (x + h) = 1

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

Simplify

= 3 (x + h)^{2}

What is the derivative of (x+h^3) ?
The derivative of (x+h^3) is 3(x+h)^2
What is the first derivative of (x+h^3) ?
The first derivative of (x+h^3) is 3(x+h)^2