Solve 2x/3*8/4+3x/2:9/16

$$\frac { 2 x } { 3 } \cdot \frac { 8 } { 4 } + \frac { 3 x } { 2 } : \frac { 9 } { 16 }$$

Evaluate

$$4x$$

Short Solution Steps

Divide 8 by 4 to get 2.

$$\frac{2x}{3}\times 2+\frac{\frac{3x}{2}}{\frac{9}{16}}$$

Express \frac{2x}{3}\times 2 as a single fraction.

$$\frac{2x\times 2}{3}+\frac{\frac{3x}{2}}{\frac{9}{16}}$$

Divide \frac{3x}{2} by \frac{9}{16} by multiplying \frac{3x}{2} by the reciprocal of \frac{9}{16}.

$$\frac{2x\times 2}{3}+\frac{3x\times 16}{2\times 9}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{2x\times 2}{3}+\frac{8x}{3}$$

Since \frac{2x\times 2}{3} and \frac{8x}{3} have the same denominator, add them by adding their numerators.

$$\frac{2x\times 2+8x}{3}$$

Do the multiplications in 2x\times 2+8x.

$$\frac{4x+8x}{3}$$

Combine like terms in 4x+8x.

$$\frac{12x}{3}$$

Divide 12x by 3 to get 4x.

$$4x$$

Differentiate w.r.t. x

$$4$$

Steps Using Definition of a Derivative

Divide 8 by 4 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x}{3}\times 2+\frac{\frac{3x}{2}}{\frac{9}{16}})$$

Express \frac{2x}{3}\times 2 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\times 2}{3}+\frac{\frac{3x}{2}}{\frac{9}{16}})$$

Divide \frac{3x}{2} by \frac{9}{16} by multiplying \frac{3x}{2} by the reciprocal of \frac{9}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\times 2}{3}+\frac{3x\times 16}{2\times 9})$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\times 2}{3}+\frac{8x}{3})$$

Since \frac{2x\times 2}{3} and \frac{8x}{3} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\times 2+8x}{3})$$

Do the multiplications in 2x\times 2+8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+8x}{3})$$

Combine like terms in 4x+8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12x}{3})$$

Divide 12x by 3 to get 4x.

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

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

$$4x^{1-1}$$

Subtract 1 from 1.

$$4x^{0}$$

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

$$4\times 1$$

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

$$4$$