Solve sqrt[3]{2^6}a^5

$$\sqrt[ 3 ] { 2 ^ { 6 } } a ^ { 5 }$$

Evaluate

$$4a^{5}$$

Solution Steps

Calculate 2 to the power of 6 and get 64.

$$\sqrt[3]{64}a^{5}$$

Calculate \sqrt[3]{64} and get 4.

$$4a^{5}$$

Differentiate w.r.t. a

$$20a^{4}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 6 and get 64.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\sqrt[3]{64}a^{5})$$

Calculate \sqrt[3]{64} and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{5})$$

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

$$5\times 4a^{5-1}$$

Multiply 5 times 4.

$$20a^{5-1}$$

Subtract 1 from 5.

$$20a^{4}$$