Solve f:1/2*3^3

$$f : \frac { 1 } { 2 } \cdot 3 ^ { 3 }$$

Evaluate

$$54f$$

Solution Steps

Divide f by \frac{1}{2} by multiplying f by the reciprocal of \frac{1}{2}.

$$f\times 2\times 3^{3}$$

Calculate 3 to the power of 3 and get 27.

$$f\times 2\times 27$$

Multiply 2 and 27 to get 54.

$$f\times 54$$

Differentiate w.r.t. f

$$54$$

Steps Using Definition of a Derivative

Divide f by \frac{1}{2} by multiplying f by the reciprocal of \frac{1}{2}.

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

Calculate 3 to the power of 3 and get 27.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times 2\times 27)$$

Multiply 2 and 27 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times 54)$$

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

$$54f^{1-1}$$

Subtract 1 from 1.

$$54f^{0}$$

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

$$54\times 1$$

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

$$54$$