Solve (4/7x^2)div5x^2

$$( \frac{ 4 }{ 7 } { x }^{ 2 } ) \div 5 { x }^{ 2 }$$

Evaluate

$$\frac{4x^{4}}{35}$$

Solution Steps

Divide \frac{4}{7}x^{2} by 5 to get \frac{4}{35}x^{2}.

$$\frac{4}{35}x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{4}{35}x^{4}$$

Differentiate w.r.t. x

$$\frac{16x^{3}}{35}$$

Steps Using Definition of a Derivative

Divide \frac{4}{7}x^{2} by 5 to get \frac{4}{35}x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{35}x^{2}x^{2})$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{35}x^{4})$$

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

$$4\times \frac{4}{35}x^{4-1}$$

Multiply 4 times \frac{4}{35}.

$$\frac{16}{35}x^{4-1}$$

Subtract 1 from 4.

$$\frac{16}{35}x^{3}$$