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Fractions & Decimals

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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$x \times x \times x \times x$$

Evaluate

$x^{4}$

Solution Steps

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

$$x^{2}xx$$

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

$$x^{3}x$$

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

$$x^{4}$$

Differentiate w.r.t. x

$4x^{3}$

Steps Using Definition of a Derivative

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

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

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

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

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

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

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

$$4x^{4-1}$$

Subtract $1$ from $4$.

$$4x^{3}$$