Solve yx^2(y^4)^2/2y^4

$$\frac { y x ^ { 2 } ( y ^ { 4 } ) ^ { 2 } } { 2 y ^ { 4 } }$$

Evaluate

$$\frac{x^{2}y^{5}}{2}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{yx^{2}y^{8}}{2y^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$\frac{y^{9}x^{2}}{2y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{x^{2}y^{5}}{2}$$

Differentiate w.r.t. x

$$xy^{5}$$