Solve 3a^42a+9+2a=

$$3 a ^ { 4 } 2 a + 9 + 2 a =$$

Evaluate

$$6a^{5}+2a+9$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$3a^{5}\times 2+9+2a$$

Multiply 3 and 2 to get 6.

$$6a^{5}+9+2a$$

Differentiate w.r.t. a

$$30a^{4}+2$$

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}.

$$4\times 6aa^{4-1}+2a^{1-1}$$

Multiply 4 times 2\times 3a.

$$24aa^{4-1}+2a^{1-1}$$

Subtract 1 from 4.

$$24aa^{3}+2a^{1-1}$$

Subtract 1 from 1.

$$24aa^{3}+2a^{0}$$

For any term t except 0, t^{0}=1.

$$24aa^{3}+2\times 1$$

For any term t, t\times 1=t and 1t=t.

$$24aa^{3}+2$$