Solve a*2a*a^2+4a^4=

$$a \cdot 2 a \cdot a ^ { 2 } + 4 a ^ { 4 } =$$

Evaluate

$$6a^{4}$$

Solution Steps

Multiply a and a to get a^{2}.

$$a^{2}\times 2a^{2}+4a^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$a^{4}\times 2+4a^{4}$$

Combine a^{4}\times 2 and 4a^{4} to get 6a^{4}.

$$6a^{4}$$

Differentiate w.r.t. a

$$24a^{3}$$

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}.

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

Subtract 1 from 1.

$$2a^{3}a^{0}+4\times 4a^{4-1}$$

Multiply 4 times 4.

$$2a^{3}a^{0}+16a^{4-1}$$

Subtract 1 from 4.

$$2a^{3}a^{0}+16a^{3}$$

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

$$2a^{3}\times 1+16a^{3}$$

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

$$2a^{3}+16a^{3}$$