Solve 14x12^225%=

$$14x { 12 }^{ 2 } 25 \% =$$

Evaluate

$$504x$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$14x\times 144\times \frac{25}{100}$$

Multiply 14 and 144 to get 2016.

$$2016x\times \frac{25}{100}$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$2016x\times \frac{1}{4}$$

Multiply 2016 and \frac{1}{4} to get \frac{2016}{4}.

$$\frac{2016}{4}x$$

Divide 2016 by 4 to get 504.

$$504x$$

Differentiate w.r.t. x

$$504$$

Steps Using Definition of a Derivative

Calculate 12 to the power of 2 and get 144.

$$\frac{\mathrm{d}}{\mathrm{d}x}(14x\times 144\times \frac{25}{100})$$

Multiply 14 and 144 to get 2016.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2016x\times \frac{25}{100})$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2016x\times \frac{1}{4})$$

Multiply 2016 and \frac{1}{4} to get \frac{2016}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2016}{4}x)$$

Divide 2016 by 4 to get 504.

$$\frac{\mathrm{d}}{\mathrm{d}x}(504x)$$

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

$$504x^{1-1}$$

Subtract 1 from 1.

$$504x^{0}$$

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

$$504\times 1$$

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

$$504$$