Solve f:|0,8|rightarrowR:f(x)=1/8xsqrt{64-x^2}

$$f : | 0,8 | \rightarrow R : f ( x ) = \frac { 1 } { 8 } x \sqrt { 64 - x ^ { 2 } }$$

Differentiate w.r.t. f

$$1.25$$

Steps Using Definition of a Derivative

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0.8 is 0.8.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f}{0.8})$$

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

$$\frac{5}{4}f^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{4}f^{0}$$

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

$$\frac{5}{4}\times 1$$

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

$$\frac{5}{4}$$

Evaluate

$$\frac{5f}{4}$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0.8 is 0.8.

$$\frac{f}{0.8}$$