Solve a/dx(-1/2a-1+c/2a^3)

$$\frac { a } { d x } ( \frac { - 1 } { 2 a } - \frac { 1 + c } { 2 a ^ { 3 } } )$$

Evaluate

$$-\frac{a^{2}+c+1}{2dxa^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 2a^{3} is 2a^{3}. Multiply \frac{-1}{2a} times \frac{a^{2}}{a^{2}}.

$$\frac{a}{dx}\left(\frac{-a^{2}}{2a^{3}}-\frac{1+c}{2a^{3}}\right)$$

Since \frac{-a^{2}}{2a^{3}} and \frac{1+c}{2a^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a}{dx}\times \frac{-a^{2}-\left(1+c\right)}{2a^{3}}$$

Do the multiplications in -a^{2}-\left(1+c\right).

$$\frac{a}{dx}\times \frac{-a^{2}-1-c}{2a^{3}}$$

Multiply \frac{a}{dx} times \frac{-a^{2}-1-c}{2a^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a\left(-a^{2}-1-c\right)}{dx\times 2a^{3}}$$

Cancel out a in both numerator and denominator.

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

Expand

$$-\frac{a^{2}+c+1}{2dxa^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 2a^{3} is 2a^{3}. Multiply \frac{-1}{2a} times \frac{a^{2}}{a^{2}}.

$$\frac{a}{dx}\left(\frac{-a^{2}}{2a^{3}}-\frac{1+c}{2a^{3}}\right)$$

Since \frac{-a^{2}}{2a^{3}} and \frac{1+c}{2a^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a}{dx}\times \frac{-a^{2}-\left(1+c\right)}{2a^{3}}$$

Do the multiplications in -a^{2}-\left(1+c\right).

$$\frac{a}{dx}\times \frac{-a^{2}-1-c}{2a^{3}}$$

Multiply \frac{a}{dx} times \frac{-a^{2}-1-c}{2a^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a\left(-a^{2}-1-c\right)}{dx\times 2a^{3}}$$

Cancel out a in both numerator and denominator.

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