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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$xxx$$

Evaluate

$x^{3}$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{1}x^{1}x^{1}$$

Use the Multiplication Rule for Exponents.

$$x^{1+1+1}$$

Add the exponents $1$ and $1$.

$$x^{2+1}$$

Add the exponents $2$ and $1$.

$$x^{3}$$

Differentiate w.r.t. x

$3x^{2}$

Steps Using Definition of a Derivative

Multiply $x$ and $x$ to get $x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x)$$

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3})$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$3x^{3-1}$$

Subtract $1$ from $3$.

$$3x^{2}$$