Solve (1+2x)^1/2 | Microsoft Math Solver

Differentiate w.r.t. x

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Algebra

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

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(2x^{1}+1\right)^{-\frac{1}{2}}\times 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}.

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

Simplify.

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

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

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

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

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

For any term t, t\times 1=t and 1t=t.