Solve (-x^4)^frac{2{4}}=

$$( - x ^ { 4 } ) ^ { \frac { 2 } { 4 } } =$$

Differentiate w.r.t. x

$$\text{Indeterminate}$$

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).

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

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}.

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

Simplify.

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

Evaluate

$$\sqrt{-x^{4}}$$

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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