Solve x^2*x^2*2x^2/1*200*9

$$\frac { x ^ { 2 } \times x ^ { 2 } \times 2 x ^ { 2 } } { 1 \times 200 \times 9 }$$

Evaluate

$$\frac{x^{6}}{900}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{x^{4}\times 2x^{2}}{1\times 200\times 9}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{x^{6}\times 2}{1\times 200\times 9}$$

Cancel out 2 in both numerator and denominator.

$$\frac{x^{6}}{9\times 100}$$

Multiply 9 and 100 to get 900.

$$\frac{x^{6}}{900}$$

Differentiate w.r.t. x

$$\frac{x^{5}}{150}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}\times 2x^{2}}{1\times 200\times 9})$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}\times 2}{1\times 200\times 9})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{9\times 100})$$

Multiply 9 and 100 to get 900.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{900})$$

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

$$6\times \frac{1}{900}x^{6-1}$$

Multiply 6 times \frac{1}{900}.

$$\frac{1}{150}x^{6-1}$$

Subtract 1 from 6.

$$\frac{1}{150}x^{5}$$