Solve 5/6x7/10x5/34x38/75

$$\frac { 5 } { 6 } x \frac { 7 } { 10 } x \frac { 5 } { 34 } x \frac { 38 } { 75 }$$

Evaluate

$$\frac{133x^{3}}{3060}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{5}{6}x^{2}\times \frac{7}{10}\times \frac{5}{34}x\times \frac{38}{75}$$

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

$$\frac{5}{6}x^{3}\times \frac{7}{10}\times \frac{5}{34}\times \frac{38}{75}$$

Multiply \frac{5}{6} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 7}{6\times 10}x^{3}\times \frac{5}{34}\times \frac{38}{75}$$

Do the multiplications in the fraction \frac{5\times 7}{6\times 10}.

$$\frac{35}{60}x^{3}\times \frac{5}{34}\times \frac{38}{75}$$

Reduce the fraction \frac{35}{60} to lowest terms by extracting and canceling out 5.

$$\frac{7}{12}x^{3}\times \frac{5}{34}\times \frac{38}{75}$$

Multiply \frac{7}{12} times \frac{5}{34} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5}{12\times 34}x^{3}\times \frac{38}{75}$$

Do the multiplications in the fraction \frac{7\times 5}{12\times 34}.

$$\frac{35}{408}x^{3}\times \frac{38}{75}$$

Multiply \frac{35}{408} times \frac{38}{75} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 38}{408\times 75}x^{3}$$

Do the multiplications in the fraction \frac{35\times 38}{408\times 75}.

$$\frac{1330}{30600}x^{3}$$

Reduce the fraction \frac{1330}{30600} to lowest terms by extracting and canceling out 10.

$$\frac{133}{3060}x^{3}$$

Differentiate w.r.t. x

$$\frac{133x^{2}}{1020}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{6}x^{2}\times \frac{7}{10}\times \frac{5}{34}x\times \frac{38}{75})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{6}x^{3}\times \frac{7}{10}\times \frac{5}{34}\times \frac{38}{75})$$

Multiply \frac{5}{6} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 7}{6\times 10}x^{3}\times \frac{5}{34}\times \frac{38}{75})$$

Do the multiplications in the fraction \frac{5\times 7}{6\times 10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35}{60}x^{3}\times \frac{5}{34}\times \frac{38}{75})$$

Reduce the fraction \frac{35}{60} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{12}x^{3}\times \frac{5}{34}\times \frac{38}{75})$$

Multiply \frac{7}{12} times \frac{5}{34} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7\times 5}{12\times 34}x^{3}\times \frac{38}{75})$$

Do the multiplications in the fraction \frac{7\times 5}{12\times 34}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35}{408}x^{3}\times \frac{38}{75})$$

Multiply \frac{35}{408} times \frac{38}{75} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35\times 38}{408\times 75}x^{3})$$

Do the multiplications in the fraction \frac{35\times 38}{408\times 75}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1330}{30600}x^{3})$$

Reduce the fraction \frac{1330}{30600} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{133}{3060}x^{3})$$

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

$$3\times \frac{133}{3060}x^{3-1}$$

Multiply 3 times \frac{133}{3060}.

$$\frac{133}{1020}x^{3-1}$$

Subtract 1 from 3.

$$\frac{133}{1020}x^{2}$$