Solve 4x^7*1/x^3

$$4 { x }^{ 7 } \times \frac{ 1 }{ { x }^{ 3 } }$$

Evaluate

$$4x^{4}$$

Solution Steps

Express 4\times \frac{1}{x^{3}} as a single fraction.

$$\frac{4}{x^{3}}x^{7}$$

Express \frac{4}{x^{3}}x^{7} as a single fraction.

$$\frac{4x^{7}}{x^{3}}$$

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

$$4x^{4}$$

Differentiate w.r.t. x

$$16x^{3}$$

Steps Using Definition of a Derivative

Express 4\times \frac{1}{x^{3}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{x^{3}}x^{7})$$

Express \frac{4}{x^{3}}x^{7} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x^{7}}{x^{3}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{4})$$

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

$$4\times 4x^{4-1}$$

Multiply 4 times 4.

$$16x^{4-1}$$

Subtract 1 from 4.

$$16x^{3}$$