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Find the derivative of $x- e^{-1}x$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $x- e^{-1}x$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve integrals of exponential functions problems step by step online.
$\lim_{h\to0}\left(\frac{x+h- e^{-1}\left(x+h\right)-\left(x- e^{-1}x\right)}{h}\right)$
Learn how to solve integrals of exponential functions problems step by step online. Find the derivative of y^3-2y^2y=x-e^(-1)x using the definition. Find the derivative of x- e^{-1}x using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is x- e^{-1}x. Substituting f(x+h) and f(x) on the limit, we get. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Divide -1 by e. Multiply the single term -\frac{1}{e} by each term of the polynomial \left(x+h\right).