Solve 20x^9y/6x*4xy^2

$$\frac { 20 x ^ { 9 } y } { 6 x \cdot 4 x y ^ { 2 } }$$

Evaluate

$$\frac{5x^{7}}{6y}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{20x^{9}y}{6x^{2}\times 4y^{2}}$$

Cancel out 2\times 2yx^{2} in both numerator and denominator.

$$\frac{5x^{7}}{2\times 3y}$$

Multiply 2 and 3 to get 6.

$$\frac{5x^{7}}{6y}$$

Differentiate w.r.t. x

$$\frac{35x^{6}}{6y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20y}{24xy^{2}}x^{9-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{6xy}x^{8})$$

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}.

$$8\times \frac{5}{6xy}x^{8-1}$$

Do the arithmetic.

$$\frac{20}{3xy}x^{7}$$