Solve 4/45x^4y^5*1/105x^5y^3

$$\frac { 4 } { 45 x ^ { 4 } y ^ { 5 } } \cdot \frac { 1 } { 105 x ^ { 5 } y ^ { 3 } }$$

Evaluate

$$\frac{4}{4725y^{8}x^{9}}$$

Solution Steps

Multiply \frac{4}{45x^{4}y^{5}} times \frac{1}{105x^{5}y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{45x^{4}y^{5}\times 105x^{5}y^{3}}$$

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

$$\frac{4}{45x^{9}y^{5}\times 105y^{3}}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{4}{45x^{9}y^{8}\times 105}$$

Multiply 45 and 105 to get 4725.

$$\frac{4}{4725x^{9}y^{8}}$$

Differentiate w.r.t. x

$$-\frac{4}{525y^{8}x^{10}}$$