Solve f(-1/2)f(3)+(0)

$$f ( - \frac { 1 } { 2 } ) f ( 3 ) + ( 0 )$$

Evaluate

$$-\frac{3f^{2}}{2}$$

Solution Steps

Multiply f and f to get f^{2}.

$$f^{2}\left(-\frac{1}{2}\right)\times 3+0$$

Express -\frac{1}{2}\times 3 as a single fraction.

$$f^{2}\times \frac{-3}{2}+0$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$f^{2}\left(-\frac{3}{2}\right)+0$$

Anything plus zero gives itself.

$$f^{2}\left(-\frac{3}{2}\right)$$

Differentiate w.r.t. f

$$-3f$$

Steps Using Definition of a Derivative

Multiply f and f to get f^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{2}\left(-\frac{1}{2}\right)\times 3+0)$$

Express -\frac{1}{2}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{2}\times \frac{-3}{2}+0)$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{2}\left(-\frac{3}{2}\right)+0)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{2}\left(-\frac{3}{2}\right))$$

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

$$2\left(-\frac{3}{2}\right)f^{2-1}$$

Multiply 2 times -\frac{3}{2}.

$$-3f^{2-1}$$

Subtract 1 from 2.

$$-3f^{1}$$

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

$$-3f$$