Solve 54/(frac{4{x}+5)-5}

$$5 \frac { 4 } { ( \frac { 4 } { x } + 5 ) - 5 }$$

Evaluate

$$5x$$

Solution Steps

Subtract 5 from 5 to get 0.

$$5\times \frac{4}{\frac{4}{x}}$$

Divide 4 by \frac{4}{x} by multiplying 4 by the reciprocal of \frac{4}{x}.

$$5\times \frac{4x}{4}$$

Cancel out 4 and 4.

$$5x$$

Differentiate w.r.t. x

$$5$$

Steps Using Definition of a Derivative

Subtract 5 from 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5\times \frac{4}{\frac{4}{x}})$$

Divide 4 by \frac{4}{x} by multiplying 4 by the reciprocal of \frac{4}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5\times \frac{4x}{4})$$

Cancel out 4 and 4.

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

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

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

Subtract 1 from 1.

$$5x^{0}$$

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

$$5\times 1$$

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

$$5$$