Solve -1^3/c^-2-21^2/2

$$- \frac { 1 ^ { 3 } } { c ^ { - 2 } } - 2 \frac { 1 ^ { 2 } } { 2 }$$

Evaluate

$$-c^{2}-1$$

Short Solution Steps

Calculate 1 to the power of 3 and get 1.

$$-\frac{1}{c^{-2}}-2\times \frac{1^{2}}{2}$$

Calculate 1 to the power of 2 and get 1.

$$-\frac{1}{c^{-2}}-2\times \frac{1}{2}$$

Multiply 2 and \frac{1}{2} to get 1.

$$-\frac{1}{c^{-2}}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{c^{-2}}{c^{-2}}.

$$-\frac{1}{c^{-2}}-\frac{c^{-2}}{c^{-2}}$$

Since -\frac{1}{c^{-2}} and \frac{c^{-2}}{c^{-2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-c^{-2}}{c^{-2}}$$

Factor the expressions that are not already factored in \frac{-1-c^{-2}}{c^{-2}}.

$$\frac{-c^{-2}\left(c^{2}+1\right)}{c^{-2}}$$

Cancel out c^{-2} in both numerator and denominator.

$$-\left(c^{2}+1\right)$$

Expand the expression.

$$-c^{2}-1$$

Differentiate w.r.t. c

$$-2c$$

Steps Using Derivative Rule for Sum

Calculate 1 to the power of 3 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-\frac{1}{c^{-2}}-2\times \frac{1^{2}}{2})$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-\frac{1}{c^{-2}}-2\times \frac{1}{2})$$

Multiply 2 and \frac{1}{2} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-\frac{1}{c^{-2}}-1)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{c^{-2}}{c^{-2}}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-\frac{1}{c^{-2}}-\frac{c^{-2}}{c^{-2}})$$

Since -\frac{1}{c^{-2}} and \frac{c^{-2}}{c^{-2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{-1-c^{-2}}{c^{-2}})$$

Factor the expressions that are not already factored in \frac{-1-c^{-2}}{c^{-2}}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{-c^{-2}\left(c^{2}+1\right)}{c^{-2}})$$

Cancel out c^{-2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-\left(c^{2}+1\right))$$

Expand the expression.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-c^{2}-1)$$

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}.

$$2\left(-1\right)c^{2-1}$$

Multiply 2 times -1.

$$-2c^{2-1}$$

Subtract 1 from 2.

$$-2c^{1}$$

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

$$-2c$$