Solve a^8+18a^4+8^8

$$a ^ { 8 } + 18 a ^ { 4 } + 8 ^ { 8 }$$

Differentiate w.r.t. a

$$8a^{3}\left(a^{4}+9\right)$$

Steps Using Derivative Rule for Sum

Calculate 8 to the power of 8 and get 16777216.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{8}+18a^{4}[phone])$$

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}.

$$8a^{8-1}+4\times 18a^{4-1}$$

Subtract 1 from 8.

$$8a^{7}+4\times 18a^{4-1}$$

Multiply 4 times 18.

$$8a^{7}+72a^{4-1}$$

Subtract 1 from 4.

$$8a^{7}+72a^{3}$$

Evaluate

$$a^{8}+18a^{4}[phone]$$

Solution Steps

Calculate 8 to the power of 8 and get 16777216.

$$a^{8}+18a^{4}[phone]$$