Solve 6x^2div9x^5

$$6 { x }^{ 2 } \div 9 { x }^{ 5 }$$

Evaluate

$$\frac{2x^{7}}{3}$$

Solution Steps

Divide 6x^{2} by 9 to get \frac{2}{3}x^{2}.

$$\frac{2}{3}x^{2}x^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{2}{3}x^{7}$$

Differentiate w.r.t. x

$$\frac{14x^{6}}{3}$$

Steps Using Definition of a Derivative

Divide 6x^{2} by 9 to get \frac{2}{3}x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x^{7})$$

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

$$7\times \frac{2}{3}x^{7-1}$$

Multiply 7 times \frac{2}{3}.

$$\frac{14}{3}x^{7-1}$$

Subtract 1 from 7.

$$\frac{14}{3}x^{6}$$