Solve 2/3x^4/x^39/1

$$\frac{ \frac{ 2 }{ 3 } { x }^{ 4 } }{ { x }^{ 3 } } \frac{ 9 }{ 1 }$$

Evaluate

$$6x$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$\frac{2}{3}x\times \frac{9}{1}$$

Anything divided by one gives itself.

$$\frac{2}{3}x\times 9$$

Multiply \frac{2}{3} and 9 to get 6.

$$6x$$

Differentiate w.r.t. x

$$6$$

Steps Using Definition of a Derivative

Cancel out x^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x\times \frac{9}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x\times 9)$$

Multiply \frac{2}{3} and 9 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x)$$

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

$$6x^{1-1}$$

Subtract 1 from 1.

$$6x^{0}$$

For any term t except 0, t^{0}=1.

$$6\times 1$$

For any term t, t\times 1=t and 1t=t.

$$6$$