Solve 7c_{3}*4c_{3}

$$7 c _ { 3 } \times 4 c _ { 3 }$$

Evaluate

$$28c_{3}^{2}$$

Solution Steps

Multiply c_{3} and c_{3} to get c_{3}^{2}.

$$7c_{3}^{2}\times 4$$

Multiply 7 and 4 to get 28.

$$28c_{3}^{2}$$

Differentiate w.r.t. c_3

$$56c_{3}$$

Steps Using Definition of a Derivative

Multiply c_{3} and c_{3} to get c_{3}^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}c_{3}}(7c_{3}^{2}\times 4)$$

Multiply 7 and 4 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}c_{3}}(28c_{3}^{2})$$

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

$$2\times 28c_{3}^{2-1}$$

Multiply 2 times 28.

$$56c_{3}^{2-1}$$

Subtract 1 from 2.

$$56c_{3}^{1}$$

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

$$56c_{3}$$