Solve (6y^2)^frac{1{4}}

$$( 6 y ^ { 2 } ) ^ { \frac { 1 } { 4 } }$$

Differentiate w.r.t. y

$$\frac{\sqrt[4]{6}sign(y)}{2\sqrt{|y|}}$$

Steps Using Chain Rule

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).

$$\frac{1}{4}\times \left(6y^{2}\right)^{\frac{1}{4}-1}\frac{\mathrm{d}}{\mathrm{d}y}(6y^{2})$$

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}.

$$\frac{1}{4}\times \left(6y^{2}\right)^{-\frac{3}{4}}\times 2\times 6y^{2-1}$$

Simplify.

$$3y^{1}\times \left(6y^{2}\right)^{-\frac{3}{4}}$$

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

$$3y\times \left(6y^{2}\right)^{-\frac{3}{4}}$$

Evaluate

$$\sqrt[4]{6}\sqrt{|y|}$$