Solve 1545x^2div5x^6

$$1545 { x }^{ 2 } \div 5 { x }^{ 6 }$$

Evaluate

$$309x^{8}$$

Solution Steps

Divide 1545x^{2} by 5 to get 309x^{2}.

$$309x^{2}x^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$309x^{8}$$

Differentiate w.r.t. x

$$2472x^{7}$$

Steps Using Definition of a Derivative

Divide 1545x^{2} by 5 to get 309x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(309x^{2}x^{6})$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(309x^{8})$$

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

$$8\times 309x^{8-1}$$

Multiply 8 times 309.

$$2472x^{8-1}$$

Subtract 1 from 8.

$$2472x^{7}$$