Lutasin ang frac{5p^{3}q^2}{45p^4q-35p^2q^3}=

$$\frac { 5 p ^ { 3 } q ^ { 2 } } { 45 p ^ { 4 } q - 35 p ^ { 2 } q ^ { 3 } } =$$

I-evaluate

$$\frac{pq}{9p^{2}-7q^{2}}$$

Maiikling Hakbang sa Solution

I-factor ang mga expression na hindi pa na-factor.

$$\frac{5q^{2}p^{3}}{5qp^{2}\left(9p^{2}-7q^{2}\right)}$$

I-cancel out ang 5qp^{2} sa parehong numerator at denominator.

$$\frac{pq}{9p^{2}-7q^{2}}$$

I-differentiate ang w.r.t. p

$$\frac{q\left(-9p^{2}-7q^{2}\right)}{\left(9p^{2}-7q^{2}\right)^{2}}$$

Mga Hakbang sa Paggamit ng Derivative Rule for Quotient

Para sa anumang dalawang madi-differentiate na function, ang derivative ng quotient ng dalawang function ay ang denominator times ang derivative ng numerator minus ang numerator times ang derivative ng denominator, lahat ng ito ay dini-divide ng denominator squared.

$$\frac{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)\frac{\mathrm{d}}{\mathrm{d}p}(5q^{2}p^{3})-5q^{2}p^{3}\frac{\mathrm{d}}{\mathrm{d}p}(45qp^{4}+\left(-35q^{3}\right)p^{2})}{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)^{2}}$$

Ang derivative ng isang polynomial ay ang kabuuan ng mga derivative ng mga term nito. Ang derivative ng anumang constant term ay 0. Ang derivative ng ax^{n} ay nax^{n-1}.

$$\frac{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)\times 3\times 5q^{2}p^{3-1}-5q^{2}p^{3}\left(4\times 45qp^{4-1}+2\left(-35q^{3}\right)p^{2-1}\right)}{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)^{2}}$$

Pasimplehin.

$$\frac{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)\times 15q^{2}p^{2}-5q^{2}p^{3}\left(180qp^{3}+\left(-70q^{3}\right)p^{1}\right)}{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)^{2}}$$

I-multiply ang 45qp^{4}+\left(-35q^{3}\right)p^{2} times 15q^{2}p^{2}.

$$\frac{45qp^{4}\times 15q^{2}p^{2}+\left(-35q^{3}\right)p^{2}\times 15q^{2}p^{2}-5q^{2}p^{3}\left(180qp^{3}+\left(-70q^{3}\right)p^{1}\right)}{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)^{2}}$$

I-multiply ang 5q^{2}p^{3} times 180qp^{3}+\left(-70q^{3}\right)p^{1}.

$$\frac{45qp^{4}\times 15q^{2}p^{2}+\left(-35q^{3}\right)p^{2}\times 15q^{2}p^{2}-\left(5q^{2}p^{3}\times 180qp^{3}+5q^{2}p^{3}\left(-70q^{3}\right)p^{1}\right)}{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)^{2}}$$

Para i-multiply ang mga power ng parehong base, idagdag ang mga exponent nito.

$$\frac{45q\times 15q^{2}p^{4+2}+\left(-35q^{3}\right)\times 15q^{2}p^{2+2}-\left(5q^{2}\times 180qp^{3+3}+5q^{2}\left(-70q^{3}\right)p^{3+1}\right)}{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)^{2}}$$

Pasimplehin.

$$\frac{675q^{3}p^{6}+\left(-525q^{5}\right)p^{4}-\left(900q^{3}p^{6}+\left(-350q^{5}\right)p^{4}\right)}{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)^{2}}$$

Pagsamahin ang magkakatulad na term.

$$\frac{\left(-225q^{3}\right)p^{6}+\left(-175q^{5}\right)p^{4}}{\left(45qp^{4}+\left(-35q^{3}\right)p^{2}\right)^{2}}$$