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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$xxxxx$$

Evaluate

$x^{5}$

Solution Steps

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

$$x^{2}xxx$$

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

$$x^{3}xx$$

To multiply powers of the same base, add their exponents. Add $3$ and $1$ to get $4$.

$$x^{4}x$$

To multiply powers of the same base, add their exponents. Add $4$ and $1$ to get $5$.

$$x^{5}$$

Differentiate w.r.t. x

$5x^{4}$

Steps Using Definition of a Derivative

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

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

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

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

To multiply powers of the same base, add their exponents. Add $3$ and $1$ to get $4$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}x)$$

To multiply powers of the same base, add their exponents. Add $4$ and $1$ to get $5$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5})$$

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

$$5x^{5-1}$$

Subtract $1$ from $5$.

$$5x^{4}$$