Solve 20x/9*36x^4/5approx

$$\frac { 20 x } { 9 } \times \frac { 36 x ^ { 4 } } { 5 } \approx$$

Evaluate

$$16x^{5}$$

Solution Steps

Multiply \frac{20x}{9} times \frac{36x^{4}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20x\times 36x^{4}}{9\times 5}$$

Cancel out 5\times 9 in both numerator and denominator.

$$4\times 4xx^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$4\times 4x^{5}$$

Multiply 4 and 4 to get 16.

$$16x^{5}$$

Differentiate w.r.t. x

$$80x^{4}$$

Steps Using Definition of a Derivative

Multiply \frac{20x}{9} times \frac{36x^{4}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20x\times 36x^{4}}{9\times 5})$$

Cancel out 5\times 9 in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4\times 4x^{5})$$

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{5})$$

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

$$5\times 16x^{5-1}$$

Multiply 5 times 16.

$$80x^{5-1}$$

Subtract 1 from 5.

$$80x^{4}$$