Solve 2x^6/7x^2div4x/7x^3

$$\frac { 2 x ^ { 6 } } { 7 x ^ { 2 } } \div \frac { 4 x } { 7 x ^ { 3 } }$$

Evaluate

$$\frac{x^{6}}{2}$$

Solution Steps

Divide \frac{2x^{6}}{7x^{2}} by \frac{4x}{7x^{3}} by multiplying \frac{2x^{6}}{7x^{2}} by the reciprocal of \frac{4x}{7x^{3}}.

$$\frac{2x^{6}\times 7x^{3}}{7x^{2}\times 4x}$$

Cancel out 2\times 7xx^{2} in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{x^{6}}{2}$$

Differentiate w.r.t. x

$$3x^{5}$$

Steps Using Definition of a Derivative

Divide \frac{2x^{6}}{7x^{2}} by \frac{4x}{7x^{3}} by multiplying \frac{2x^{6}}{7x^{2}} by the reciprocal of \frac{4x}{7x^{3}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{6}\times 7x^{3}}{7x^{2}\times 4x})$$

Cancel out 2\times 7xx^{2} in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

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

$$6\times \frac{1}{2}x^{6-1}$$

Multiply 6 times \frac{1}{2}.

$$3x^{6-1}$$

Subtract 1 from 6.

$$3x^{5}$$