Solve 10x^9/8*2/15x^3

$$\frac { 10 x ^ { 9 } } { 8 } \times \frac { 2 } { 15 x ^ { 3 } }$$

Evaluate

$$\frac{x^{6}}{6}$$

Solution Steps

Divide 10x^{9} by 8 to get \frac{5}{4}x^{9}.

$$\frac{5}{4}x^{9}\times \frac{2}{15x^{3}}$$

Multiply \frac{5}{4} times \frac{2}{15x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 2}{4\times 15x^{3}}x^{9}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{1}{2\times 3x^{3}}x^{9}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{6x^{3}}x^{9}$$

Express \frac{1}{6x^{3}}x^{9} as a single fraction.

$$\frac{x^{9}}{6x^{3}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{x^{6}}{6}$$

Differentiate w.r.t. x

$$x^{5}$$

Steps Using Definition of a Derivative

Divide 10x^{9} by 8 to get \frac{5}{4}x^{9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{4}x^{9}\times \frac{2}{15x^{3}})$$

Multiply \frac{5}{4} times \frac{2}{15x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 2}{4\times 15x^{3}}x^{9})$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2\times 3x^{3}}x^{9})$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{6x^{3}}x^{9})$$

Express \frac{1}{6x^{3}}x^{9} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{9}}{6x^{3}})$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{6})$$

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

$$6\times \frac{1}{6}x^{6-1}$$

Multiply 6 times \frac{1}{6}.

$$x^{6-1}$$

Subtract 1 from 6.

$$x^{5}$$