Solve 53-c^3quad3quad61quad183quad370

$$53 - c ^ { 3 } \quad 3 \quad 61 \quad 183 \quad 370$$

Evaluate

$$53-12390930c^{3}$$

Solution Steps

Multiply 3 and 61 to get 183.

$$53-c^{3}\times 183\times 183\times 370$$

Multiply 183 and 183 to get 33489.

$$53-c^{3}\times 33489\times 370$$

Multiply 33489 and 370 to get 12390930.

$$53-c^{3}\times 12390930$$

Multiply -1 and 12390930 to get -12390930.

$$53-12390930c^{3}$$

Differentiate w.r.t. c

$$-37172790c^{2}$$

Steps Using Derivative Rule for Sum

Multiply 3 and 61 to get 183.

$$\frac{\mathrm{d}}{\mathrm{d}c}(53-c^{3}\times 183\times 183\times 370)$$

Multiply 183 and 183 to get 33489.

$$\frac{\mathrm{d}}{\mathrm{d}c}(53-c^{3}\times 33489\times 370)$$

Multiply 33489 and 370 to get 12390930.

$$\frac{\mathrm{d}}{\mathrm{d}c}(53-c^{3}\times 12390930)$$

Multiply -1 and 12390930 to get -12390930.

$$\frac{\mathrm{d}}{\mathrm{d}c}(53-12390930c^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\left(-12390930\right)c^{3-1}$$

Multiply 3 times -12390930.

$$-37172790c^{3-1}$$

Subtract 1 from 3.

$$-37172790c^{2}$$