Solve (A)2^3*3^3*7*11

$$( A ) 2 ^ { 3 } \times 3 ^ { 3 } \times 7 \times 11$$

Evaluate

$$16632A$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$A\times 8\times 3^{3}\times 7\times 11$$

Calculate 3 to the power of 3 and get 27.

$$A\times 8\times 27\times 7\times 11$$

Multiply 8 and 27 to get 216.

$$A\times 216\times 7\times 11$$

Multiply 216 and 7 to get 1512.

$$A\times 1512\times 11$$

Multiply 1512 and 11 to get 16632.

$$A\times 16632$$

Differentiate w.r.t. A

$$16632$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 8\times 3^{3}\times 7\times 11)$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 8\times 27\times 7\times 11)$$

Multiply 8 and 27 to get 216.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 216\times 7\times 11)$$

Multiply 216 and 7 to get 1512.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 1512\times 11)$$

Multiply 1512 and 11 to get 16632.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 16632)$$

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

$$16632A^{1-1}$$

Subtract 1 from 1.

$$16632A^{0}$$

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

$$16632\times 1$$

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

$$16632$$