Solve fquad4quad4quad4quad5quad5

$$f \quad 4 \quad 4 \quad 4 \quad 5 \quad 5$$

Evaluate

$$400f_{4}$$

Solution Steps

Multiply 4 and 4 to get 16.

$$f_{4}\times 16\times 5\times 5$$

Multiply 16 and 5 to get 80.

$$f_{4}\times 80\times 5$$

Multiply 80 and 5 to get 400.

$$f_{4}\times 400$$

Differentiate w.r.t. f_4

$$400$$

Steps Using Definition of a Derivative

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}f_{4}}(f_{4}\times 16\times 5\times 5)$$

Multiply 16 and 5 to get 80.

$$\frac{\mathrm{d}}{\mathrm{d}f_{4}}(f_{4}\times 80\times 5)$$

Multiply 80 and 5 to get 400.

$$\frac{\mathrm{d}}{\mathrm{d}f_{4}}(f_{4}\times 400)$$

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

$$400f_{4}^{1-1}$$

Subtract 1 from 1.

$$400f_{4}^{0}$$

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

$$400\times 1$$

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

$$400$$