Solve 40x/5*x^4/8x^2

$$\frac { 40 x } { 5 } \cdot \frac { x ^ { 4 } } { 8 x ^ { 2 } }$$

Evaluate

$$x^{3}$$

Solution Steps

Divide 40x by 5 to get 8x.

$$8x\times \frac{x^{4}}{8x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$8x\times \frac{x^{2}}{8}$$

Cancel out 8 and 8.

$$x^{2}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Steps Using Definition of a Derivative

Divide 40x by 5 to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x\times \frac{x^{4}}{8x^{2}})$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x\times \frac{x^{2}}{8})$$

Cancel out 8 and 8.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Subtract 1 from 3.

$$3x^{2}$$