Solve 10xy2x-5/2x^2y^2

$$10 x y 2 x \frac { - 5 } { 2 } x ^ { 2 } y ^ { 2 }$$

Evaluate

$$-25y_{2}y^{2}x^{4}$$

Solution Steps

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

$$10x^{2}y_{2}\times \frac{-5}{2}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$10x^{4}y_{2}\times \frac{-5}{2}y^{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$10x^{4}y_{2}\left(-\frac{5}{2}\right)y^{2}$$

Multiply 10 and -\frac{5}{2} to get -25.

$$-25x^{4}y_{2}y^{2}$$

Differentiate w.r.t. x

$$-100y_{2}y^{2}x^{3}$$