Solve 6x^26y^-7/22x^9y^7

$$\frac{ 6 { x }^{ 26 } { y }^{ -7 } }{ 22 { x }^{ 9 } { y }^{ 7 } }$$

Evaluate

$$\frac{3x^{17}}{11y^{14}}$$

Solution Steps

Cancel out 2x^{9} in both numerator and denominator.

$$\frac{3y^{-7}x^{17}}{11y^{7}}$$

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

$$\frac{3x^{17}}{11y^{14}}$$

Differentiate w.r.t. x

$$\frac{51x^{16}}{11y^{14}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{y^{7}\times 22y^{7}}x^{26-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{11y^{14}}x^{17})$$

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}.

$$17\times \frac{3}{11y^{14}}x^{17-1}$$

Do the arithmetic.

$$\frac{51}{11y^{14}}x^{16}$$