Solve 3/3xy2y/6x

$$\frac { 3 } { 3 x y } \frac { 2 y } { 6 x }$$

Evaluate

$$\frac{1}{3x^{2}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3}{3xy}\times \frac{y}{3x}$$

Multiply \frac{3}{3xy} times \frac{y}{3x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3y}{3xy\times 3x}$$

Cancel out 3y in both numerator and denominator.

$$\frac{1}{3xx}$$

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

$$\frac{1}{3x^{2}}$$

Differentiate w.r.t. x

$$-\frac{2}{3x^{3}}$$

Steps Using Chain Rule

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{3xy}\times \frac{y}{3x})$$

Multiply \frac{3}{3xy} times \frac{y}{3x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y}{3xy\times 3x})$$

Cancel out 3y in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3xx})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3x^{2}})$$

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(3x^{2}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-\left(3x^{2}\right)^{-2}\times 2\times 3x^{2-1}$$

Simplify.

$$-6x^{1}\times \left(3x^{2}\right)^{-2}$$

For any term t, t^{1}=t.

$$-6x\times \left(3x^{2}\right)^{-2}$$