Solve 19x/y^3div3xy/4

$$\frac { 19 x } { y ^ { 3 } } \div \frac { 3 x y } { 4 }$$

Evaluate

$$\frac{76}{3y^{4}}$$

Solution Steps

Divide \frac{19x}{y^{3}} by \frac{3xy}{4} by multiplying \frac{19x}{y^{3}} by the reciprocal of \frac{3xy}{4}.

$$\frac{19x\times 4}{y^{3}\times 3xy}$$

Cancel out x in both numerator and denominator.

$$\frac{4\times 19}{3yy^{3}}$$

Multiply 4 and 19 to get 76.

$$\frac{76}{3yy^{3}}$$

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

$$\frac{76}{3y^{4}}$$

Differentiate w.r.t. y

$$-\frac{304}{3y^{5}}$$