Solve 13(2x^3)(3x^2)/(x^2)^3

$$13 \frac { ( 2 x ^ { 3 } ) ( 3 x ^ { 2 } ) } { ( x ^ { 2 } ) ^ { 3 } }$$

Evaluate

$$\frac{78}{x}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$13\times \frac{2x^{5}\times 3}{\left(x^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$13\times \frac{2x^{5}\times 3}{x^{6}}$$

Cancel out x^{5} in both numerator and denominator.

$$13\times \frac{2\times 3}{x}$$

Multiply 2 and 3 to get 6.

$$13\times \frac{6}{x}$$

Express 13\times \frac{6}{x} as a single fraction.

$$\frac{13\times 6}{x}$$

Multiply 13 and 6 to get 78.

$$\frac{78}{x}$$

Differentiate w.r.t. x

$$-\frac{78}{x^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13\times \frac{2x^{5}\times 3}{\left(x^{2}\right)^{3}})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13\times \frac{2x^{5}\times 3}{x^{6}})$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13\times \frac{2\times 3}{x})$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13\times \frac{6}{x})$$

Express 13\times \frac{6}{x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{13\times 6}{x})$$

Multiply 13 and 6 to get 78.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{78}{x})$$

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

$$-78x^{-1-1}$$

Subtract 1 from -1.

$$-78x^{-2}$$