Solve 20x^3y^8/30x^-3y^7

$$\frac { 20 x ^ { 3 } y ^ { 8 } } { 30 x ^ { - 3 } y ^ { 7 } }$$

Evaluate

$$\frac{2yx^{6}}{3}$$

Solution Steps

Cancel out 10y^{7} in both numerator and denominator.

$$\frac{2yx^{3}}{3x^{-3}}$$

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

$$\frac{2yx^{6}}{3}$$

Differentiate w.r.t. x

$$4yx^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20y^{8}}{30y^{7}}x^{3-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y}{3}x^{6})$$

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}.

$$6\times \frac{2y}{3}x^{6-1}$$

Do the arithmetic.

$$4yx^{5}$$