Solve 5x^7/2div15x^3/6

$$\frac { 5 x ^ { 7 } } { 2 } \div \frac { 15 x ^ { 3 } } { 6 }$$

Evaluate

$$x^{4}$$

Solution Steps

Divide \frac{5x^{7}}{2} by \frac{15x^{3}}{6} by multiplying \frac{5x^{7}}{2} by the reciprocal of \frac{15x^{3}}{6}.

$$\frac{5x^{7}\times 6}{2\times 15x^{3}}$$

Cancel out 2\times 3\times 5x^{3} in both numerator and denominator.

$$x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Steps Using Definition of a Derivative

Divide \frac{5x^{7}}{2} by \frac{15x^{3}}{6} by multiplying \frac{5x^{7}}{2} by the reciprocal of \frac{15x^{3}}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x^{7}\times 6}{2\times 15x^{3}})$$

Cancel out 2\times 3\times 5x^{3} in both numerator and denominator.

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

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

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

Subtract 1 from 4.

$$4x^{3}$$