Solve 2x^2*x^2/16x^5

$$\frac { 2 x ^ { 2 } \times x ^ { 2 } } { 16 x ^ { 5 } }$$

Evaluate

$$\frac{1}{8x}$$

Solution Steps

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

$$\frac{2x^{4}}{16x^{5}}$$

Cancel out 2x^{4} in both numerator and denominator.

$$\frac{1}{8x}$$

Differentiate w.r.t. x

$$-\frac{1}{8x^{2}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}}{16}x^{2-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{8}x^{-3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-3\times \frac{x^{2}}{8}x^{-3-1}$$

Do the arithmetic.

$$\left(-\frac{3x^{2}}{8}\right)x^{-4}$$