Solve y^4/4x^3y^4

$$\frac { y ^ { 4 } } { 4 x ^ { 3 } y ^ { 4 } }$$

Differentiate w.r.t. x

$$-\frac{3}{4x^{4}}$$

Steps Using Chain Rule

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4x^{3}})$$

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).

$$-\left(4x^{3}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3})$$

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}.

$$-\left(4x^{3}\right)^{-2}\times 3\times 4x^{3-1}$$

Simplify.

$$-12x^{2}\times \left(4x^{3}\right)^{-2}$$

Evaluate

$$\frac{1}{4x^{3}}$$

Solution Steps

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

$$\frac{1}{4x^{3}}$$