Solve x/frac{3{9}}+x/25/100+frac{x/2}{10}+frac{frac{x}{15}}{90}

$$\frac{ x }{ \frac{ 3 }{ 9 } } + \frac{ \frac{ x }{ 25 } }{ 100 } + \frac{ \frac{ x }{ 2 } }{ 10 } + \frac{ \frac{ x }{ 15 } }{ 90 }$$

Evaluate

$$\frac{51488x}{16875}$$

Solution Steps

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

$$\frac{x\times 9}{3}+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Divide x\times 9 by 3 to get x\times 3.

$$x\times 3+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Express \frac{\frac{x}{25}}{100} as a single fraction.

$$x\times 3+\frac{x}{25\times 100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Multiply 25 and 100 to get 2500.

$$x\times 3+\frac{x}{2500}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Combine x\times 3 and \frac{x}{2500} to get \frac{7501}{2500}x.

$$\frac{7501}{2500}x+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Express \frac{\frac{x}{2}}{10} as a single fraction.

$$\frac{7501}{2500}x+\frac{x}{2\times 10}+\frac{\frac{x}{15}}{90}$$

Multiply 2 and 10 to get 20.

$$\frac{7501}{2500}x+\frac{x}{20}+\frac{\frac{x}{15}}{90}$$

Combine \frac{7501}{2500}x and \frac{x}{20} to get \frac{3813}{1250}x.

$$\frac{3813}{1250}x+\frac{\frac{x}{15}}{90}$$

Express \frac{\frac{x}{15}}{90} as a single fraction.

$$\frac{3813}{1250}x+\frac{x}{15\times 90}$$

Multiply 15 and 90 to get 1350.

$$\frac{3813}{1250}x+\frac{x}{1350}$$

Combine \frac{3813}{1250}x and \frac{x}{1350} to get \frac{51488}{16875}x.

$$\frac{51488}{16875}x$$

Differentiate w.r.t. x

$$\frac{51488}{16875} = 3\frac{863}{16875} = 3.051140740740741$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 9}{3}+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Divide x\times 9 by 3 to get x\times 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Express \frac{\frac{x}{25}}{100} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{x}{25\times 100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Multiply 25 and 100 to get 2500.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{x}{2500}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Combine x\times 3 and \frac{x}{2500} to get \frac{7501}{2500}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Express \frac{\frac{x}{2}}{10} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{x}{2\times 10}+\frac{\frac{x}{15}}{90})$$

Multiply 2 and 10 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{x}{20}+\frac{\frac{x}{15}}{90})$$

Combine \frac{7501}{2500}x and \frac{x}{20} to get \frac{3813}{1250}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{\frac{x}{15}}{90})$$

Express \frac{\frac{x}{15}}{90} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{x}{15\times 90})$$

Multiply 15 and 90 to get 1350.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{x}{1350})$$

Combine \frac{3813}{1250}x and \frac{x}{1350} to get \frac{51488}{16875}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{51488}{16875}x)$$

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

$$\frac{51488}{16875}x^{1-1}$$

Subtract 1 from 1.

$$\frac{51488}{16875}x^{0}$$

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

$$\frac{51488}{16875}\times 1$$

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

$$\frac{51488}{16875}$$