Skip to main content
Evaluate
Tick mark Image
Differentiate w.r.t. x
Tick mark Image
Graph

Similar Problems from Web Search

Share

\frac{x}{x\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{1}{x+1}
Cancel out x in both numerator and denominator.
\frac{\left(x^{2}+x^{1}\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+x^{1})}{\left(x^{2}+x^{1}\right)^{2}}
For any two differentiable functions, the derivative of the quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.
\frac{\left(x^{2}+x^{1}\right)x^{1-1}-x^{1}\left(2x^{2-1}+x^{1-1}\right)}{\left(x^{2}+x^{1}\right)^{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{\left(x^{2}+x^{1}\right)x^{0}-x^{1}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}\right)^{2}}
Simplify.
\frac{x^{2}x^{0}+x^{1}x^{0}-x^{1}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}\right)^{2}}
Multiply x^{2}+x^{1} times x^{0}.
\frac{x^{2}x^{0}+x^{1}x^{0}-\left(x^{1}\times 2x^{1}+x^{1}x^{0}\right)}{\left(x^{2}+x^{1}\right)^{2}}
Multiply x^{1} times 2x^{1}+x^{0}.
\frac{x^{2}+x^{1}-\left(2x^{1+1}+x^{1}\right)}{\left(x^{2}+x^{1}\right)^{2}}
To multiply powers of the same base, add their exponents.
\frac{x^{2}+x^{1}-\left(2x^{2}+x^{1}\right)}{\left(x^{2}+x^{1}\right)^{2}}
Simplify.
\frac{-x^{2}}{\left(x^{2}+x^{1}\right)^{2}}
Combine like terms.
\frac{-x^{2}}{\left(x^{2}+x\right)^{2}}
For any term t, t^{1}=t.