Solve 5%*9^2x

$$5 \% \times { 9 }^{ 2 } x$$

Evaluate

$$\frac{81x}{20}$$

Solution Steps

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1}{20}\times 9^{2}x$$

Calculate 9 to the power of 2 and get 81.

$$\frac{1}{20}\times 81x$$

Multiply \frac{1}{20} and 81 to get \frac{81}{20}.

$$\frac{81}{20}x$$

Differentiate w.r.t. x

$$\frac{81}{20} = 4\frac{1}{20} = 4.05$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{20}\times 9^{2}x)$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{20}\times 81x)$$

Multiply \frac{1}{20} and 81 to get \frac{81}{20}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{81}{20}x)$$

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

$$\frac{81}{20}x^{1-1}$$

Subtract 1 from 1.

$$\frac{81}{20}x^{0}$$

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

$$\frac{81}{20}\times 1$$

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

$$\frac{81}{20}$$