Solve 10x/5*x^6/2x^3

$$\frac { 10 x } { 5 } \cdot \frac { x ^ { 6 } } { 2 x ^ { 3 } }$$

Evaluate

$$x^{4}$$

Solution Steps

Divide 10x by 5 to get 2x.

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

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

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

Cancel out 2 and 2.

$$x^{3}x$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Steps Using Definition of a Derivative

Divide 10x by 5 to get 2x.

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

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

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

Cancel out 2 and 2.

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

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

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

Subtract 1 from 4.

$$4x^{3}$$