Solve 2^4a^6-0.125^4

$${ 2 }^{ 4 } { a }^{ 6 } { -0.125 }^{ 4 }$$

Evaluate

$$\frac{a^{6}}{256}$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$16a^{6}\left(-0.125\right)^{4}$$

Calculate -0.125 to the power of 4 and get 0.000244140625.

$$16a^{6}\times 0.000244140625$$

Multiply 16 and 0.000244140625 to get 0.00390625.

$$0.00390625a^{6}$$

Differentiate w.r.t. a

$$\frac{3a^{5}}{128}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(16a^{6}\left(-0.125\right)^{4})$$

Calculate -0.125 to the power of 4 and get 0.000244140625.

$$\frac{\mathrm{d}}{\mathrm{d}a}(16a^{6}\times 0.000244140625)$$

Multiply 16 and 0.000244140625 to get 0.00390625.

$$\frac{\mathrm{d}}{\mathrm{d}a}(0.00390625a^{6})$$

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

$$6\times 0.00390625a^{6-1}$$

Multiply 6 times 0.00390625.

$$0.0234375a^{6-1}$$

Subtract 1 from 6.

$$0.0234375a^{5}$$