Solve 2^4x^35^-2

$$2 ^ { 4 } x ^ { 3 } 5 ^ { - 2 }$$

Evaluate

$$\frac{16x^{3}}{25}$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$16x^{3}\times 5^{-2}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$16x^{3}\times \frac{1}{25}$$

Multiply 16 and \frac{1}{25} to get \frac{16}{25}.

$$\frac{16}{25}x^{3}$$

Differentiate w.r.t. x

$$\frac{48x^{2}}{25}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{3}\times 5^{-2})$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{3}\times \frac{1}{25})$$

Multiply 16 and \frac{1}{25} to get \frac{16}{25}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{25}x^{3})$$

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

$$3\times \frac{16}{25}x^{3-1}$$

Multiply 3 times \frac{16}{25}.

$$\frac{48}{25}x^{3-1}$$

Subtract 1 from 3.

$$\frac{48}{25}x^{2}$$