Solve f(x)=9/(frac{9{x}+5)-5}

$$f ( x ) = \frac { 9 } { ( \frac { 9 } { x } + 5 ) - 5 }$$

Evaluate

$$x$$

Solution Steps

Subtract 5 from 5 to get 0.

$$\frac{9}{\frac{9}{x}}$$

Divide 9 by \frac{9}{x} by multiplying 9 by the reciprocal of \frac{9}{x}.

$$\frac{9x}{9}$$

Cancel out 9 and 9.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Subtract 5 from 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{\frac{9}{x}})$$

Divide 9 by \frac{9}{x} by multiplying 9 by the reciprocal of \frac{9}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x}{9})$$

Cancel out 9 and 9.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$