Solve -5/4a^5-3/7a^5-1/2a^5

$$- \frac { 5 } { 4 } a ^ { 5 } - \frac { 3 } { 7 } a ^ { 5 } - \frac { 1 } { 2 } a ^ { 5 }$$

Evaluate

$$-\frac{61a^{5}}{28}$$

Solution Steps

Combine -\frac{5}{4}a^{5} and -\frac{3}{7}a^{5} to get -\frac{47}{28}a^{5}.

$$-\frac{47}{28}a^{5}-\frac{1}{2}a^{5}$$

Combine -\frac{47}{28}a^{5} and -\frac{1}{2}a^{5} to get -\frac{61}{28}a^{5}.

$$-\frac{61}{28}a^{5}$$

Differentiate w.r.t. a

$$-\frac{305a^{4}}{28}$$

Steps Using Definition of a Derivative

Combine -\frac{5}{4}a^{5} and -\frac{3}{7}a^{5} to get -\frac{47}{28}a^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-\frac{47}{28}a^{5}-\frac{1}{2}a^{5})$$

Combine -\frac{47}{28}a^{5} and -\frac{1}{2}a^{5} to get -\frac{61}{28}a^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-\frac{61}{28}a^{5})$$

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

$$5\left(-\frac{61}{28}\right)a^{5-1}$$

Multiply 5 times -\frac{61}{28}.

$$-\frac{305}{28}a^{5-1}$$

Subtract 1 from 5.

$$-\frac{305}{28}a^{4}$$