Solve dy/dxtext{of}f(x)=-4sqrt{x}+1/2x^2

$$\frac { d y } { d x } \text { of } f ( x ) = - 4 \sqrt { x } + \frac { 1 } { 2 x ^ { 2 } }$$

Solve for f

$$f\in \mathrm{R}$$

$$x = \frac{2 ^ {\frac{4}{5}}}{4} = 0.43527528164806206$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)fx\times 2x^{2}=-4\sqrt{x}\times 2x^{2}+1$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)fx^{3}\times 2=-4\sqrt{x}\times 2x^{2}+1$$

Multiply -4 and 2 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)fx^{3}\times 2=-8\sqrt{x}x^{2}+1$$

The equation is in standard form.

$$0=-8\sqrt{x}x^{2}+1$$

This is false for any f.

$$f\in$$

Solve for x

$$x = \frac{2 ^ {\frac{4}{5}}}{4} = 0.43527528164806206$$