Solve 3/4x^2:1/4x

$$\frac { 3 } { 4 } x ^ { 2 } : \frac { 1 } { 4 } x$$

Evaluate

$$3x^{3}$$

Solution Steps

Divide \frac{3}{4}x^{2} by \frac{1}{4} by multiplying \frac{3}{4}x^{2} by the reciprocal of \frac{1}{4}.

$$\frac{3}{4}x^{2}\times 4x$$

Multiply \frac{3}{4} and 4 to get 3.

$$3x^{2}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3x^{3}$$

Differentiate w.r.t. x

$$9x^{2}$$

Steps Using Definition of a Derivative

Divide \frac{3}{4}x^{2} by \frac{1}{4} by multiplying \frac{3}{4}x^{2} by the reciprocal of \frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4}x^{2}\times 4x)$$

Multiply \frac{3}{4} and 4 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}x)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

$$3\times 3x^{3-1}$$

Multiply 3 times 3.

$$9x^{3-1}$$

Subtract 1 from 3.

$$9x^{2}$$