Solve a^5+5/6a^3*3/5a^2=

$$a ^ { 5 } + \frac { 5 } { 6 } a ^ { 3 } \cdot \frac { 3 } { 5 } a ^ { 2 } =$$

Evaluate

$$\frac{3a^{5}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$a^{5}+\frac{5}{6}a^{5}\times \frac{3}{5}$$

Multiply \frac{5}{6} and \frac{3}{5} to get \frac{1}{2}.

$$a^{5}+\frac{1}{2}a^{5}$$

Combine a^{5} and \frac{1}{2}a^{5} to get \frac{3}{2}a^{5}.

$$\frac{3}{2}a^{5}$$

Differentiate w.r.t. a

$$\frac{15a^{4}}{2}$$

Steps Using Derivative Rule for Sum

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}.

$$5a^{5-1}+3\times \frac{\frac{5}{2}a^{2}}{5}a^{3-1}$$

Subtract 1 from 5.

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

Multiply 3 times \frac{3}{5}\times \frac{5}{6}a^{2}.

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

Subtract 1 from 3.

$$5a^{4}+\frac{3a^{2}}{2}a^{2}$$