Solve f(x):1/x+5

$$f ( x ) : \frac { 1 } { x + 5 }$$

Differentiate w.r.t. x

$$f\left(2x+5\right)$$

Steps Using Derivative Rule for Sum

Divide fx by \frac{1}{x+5} by multiplying fx by the reciprocal of \frac{1}{x+5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(fx\left(x+5\right))$$

Use the distributive property to multiply fx by x+5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(fx^{2}+5fx)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2fx^{2-1}+5fx^{1-1}$$

Subtract 1 from 2.

$$2fx^{1}+5fx^{1-1}$$

Subtract 1 from 1.

$$2fx^{1}+5fx^{0}$$

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

$$2fx+5fx^{0}$$

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

$$2fx+5f\times 1$$

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

$$2fx+5f$$

Evaluate

$$fx\left(x+5\right)$$