Solve d/dxleft(left(2x+1right)^-0.5right)

$$\frac{d}{d x } \left( { \left(2x+1 \right) }^{ -0.5 } \right)$$

Evaluate

$$-\frac{1}{\left(2x+1\right)^{1.5}}$$

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).

$$-0.5\left(2x^{1}+1\right)^{-0.5-1}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+1)$$

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}.

$$-0.5\left(2x^{1}+1\right)^{-1.5}\times 2x^{1-1}$$

Simplify.

$$-x^{0}\left(2x^{1}+1\right)^{-1.5}$$

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

$$-x^{0}\left(2x+1\right)^{-1.5}$$

For any term t except 0, t^{0}=1.

$$-\left(2x+1\right)^{-1.5}$$

Differentiate w.r.t. x

$$\frac{3}{\left(2x+1\right)^{2.5}}$$