Solve 8x^30y^-8/28x^9y^8

$$\frac{ 8 { x }^{ 30 } { y }^{ -8 } }{ 28 { x }^{ 9 } { y }^{ 8 } }$$

Evaluate

$$\frac{2x^{21}}{7y^{16}}$$

Solution Steps

Cancel out 4x^{9} in both numerator and denominator.

$$\frac{2y^{-8}x^{21}}{7y^{8}}$$

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

$$\frac{2x^{21}}{7y^{16}}$$

Differentiate w.r.t. x

$$\frac{6x^{20}}{y^{16}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{y^{8}\times 28y^{8}}x^{30-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{7y^{16}}x^{21})$$

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}.

$$21\times \frac{2}{7y^{16}}x^{21-1}$$

Do the arithmetic.

$$\frac{6}{y^{16}}x^{20}$$