Solve (5/8x^{2}z^{3}t^{2}-3/8x^{2}z^{3}t^{2}+5/2x^{2}z^{3}t^{2}+5/4x^{2}z^{3}t^2-3x^2z^3t^2)

$$( \frac { 5 } { 8 } x ^ { 2 } z ^ { 3 } t ^ { 2 } - \frac { 3 } { 8 } x ^ { 2 } z ^ { 3 } t ^ { 2 } + \frac { 5 } { 2 } x ^ { 2 } z ^ { 3 } t ^ { 2 } + \frac { 5 } { 4 } x ^ { 2 } z ^ { 3 } t ^ { 2 } - 3 x ^ { 2 } z ^ { 3 } t ^ { 2 } )$$

Evaluate

$$z^{3}\left(tx\right)^{2}$$

Solution Steps

Combine \frac{5}{8}x^{2}z^{3}t^{2} and -\frac{3}{8}x^{2}z^{3}t^{2} to get \frac{1}{4}x^{2}z^{3}t^{2}.

$$\frac{1}{4}x^{2}z^{3}t^{2}+\frac{5}{2}x^{2}z^{3}t^{2}+\frac{5}{4}x^{2}z^{3}t^{2}-3x^{2}z^{3}t^{2}$$

Combine \frac{1}{4}x^{2}z^{3}t^{2} and \frac{5}{2}x^{2}z^{3}t^{2} to get \frac{11}{4}x^{2}z^{3}t^{2}.

$$\frac{11}{4}x^{2}z^{3}t^{2}+\frac{5}{4}x^{2}z^{3}t^{2}-3x^{2}z^{3}t^{2}$$

Combine \frac{11}{4}x^{2}z^{3}t^{2} and \frac{5}{4}x^{2}z^{3}t^{2} to get 4x^{2}z^{3}t^{2}.

$$4x^{2}z^{3}t^{2}-3x^{2}z^{3}t^{2}$$

Combine 4x^{2}z^{3}t^{2} and -3x^{2}z^{3}t^{2} to get x^{2}z^{3}t^{2}.

$$x^{2}z^{3}t^{2}$$

Differentiate w.r.t. x

$$2xt^{2}z^{3}$$