Solve 30div4/3x

$$30 \div \frac { 4 } { 3 } x$$

Evaluate

$$\frac{45x}{2}$$

Solution Steps

Divide 30 by \frac{4}{3} by multiplying 30 by the reciprocal of \frac{4}{3}.

$$30\times \frac{3}{4}x$$

Express 30\times \frac{3}{4} as a single fraction.

$$\frac{30\times 3}{4}x$$

Multiply 30 and 3 to get 90.

$$\frac{90}{4}x$$

Reduce the fraction \frac{90}{4} to lowest terms by extracting and canceling out 2.

$$\frac{45}{2}x$$

Differentiate w.r.t. x

$$\frac{45}{2} = 22\frac{1}{2} = 22.5$$

Steps Using Definition of a Derivative

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

$$\frac{45}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{45}{2}x^{0}$$

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

$$\frac{45}{2}\times 1$$

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

$$\frac{45}{2}$$