Solve frac{y^{3}xy^3xy^4}{yxy^3xy^5}

$$\frac { y ^ { 3 } x y ^ { 3 } x y ^ { 4 } } { y x y ^ { 3 } x y ^ { 5 } }$$

Evaluate

$$y$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{y^{6}xxy^{4}}{yxy^{3}xy^{5}}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{y^{10}xx}{yxy^{3}xy^{5}}$$

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

$$\frac{y^{10}x^{2}}{yxy^{3}xy^{5}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{y^{10}x^{2}}{y^{4}xxy^{5}}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{y^{10}x^{2}}{y^{9}xx}$$

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

$$\frac{y^{10}x^{2}}{y^{9}x^{2}}$$

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

$$y$$

Differentiate w.r.t. y

$$1$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{xxy^{3}y^{4}}{xxy^{3}y^{5}}y^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{y}y^{2})$$

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}.

$$2\times \frac{1}{y}y^{2-1}$$

Do the arithmetic.

$$\frac{2}{y}y^{1}$$

For any term t, t^{1}=t.

$$\frac{2}{y}y$$