Solve 5x*(-1/3ax)*(-225axy)*(12x^2y^2)

$$5 x \cdot ( - \frac { 1 } { 3 } a x ) \cdot ( - 225 a x y ) \cdot ( 12 x ^ { 2 } y ^ { 2 } )$$

Evaluate

$$4500a^{2}y^{3}x^{5}$$

Solution Steps

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

$$5x^{2}\left(-\frac{1}{3}\right)a\left(-225\right)axy\times 12x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$5x^{3}\left(-\frac{1}{3}\right)a\left(-225\right)ay\times 12x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$5x^{5}\left(-\frac{1}{3}\right)a\left(-225\right)ay\times 12y^{2}$$

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

$$5x^{5}\left(-\frac{1}{3}\right)a^{2}\left(-225\right)y\times 12y^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$5x^{5}\left(-\frac{1}{3}\right)a^{2}\left(-225\right)y^{3}\times 12$$

Multiply 5 and -\frac{1}{3} to get -\frac{5}{3}.

$$-\frac{5}{3}x^{5}a^{2}\left(-225\right)y^{3}\times 12$$

Multiply -\frac{5}{3} and -225 to get 375.

$$375x^{5}a^{2}y^{3}\times 12$$

Multiply 375 and 12 to get 4500.

$$4500x^{5}a^{2}y^{3}$$

Differentiate w.r.t. x

$$22500a^{2}y^{3}x^{4}$$