WebThe derivative of e 2x with respect to x is 2e 2x.We write this mathematically as d/dx (e 2x) = 2e 2x (or) (e 2x)' = 2e 2x.Here, f(x) = e 2x is an exponential function as the base is 'e' is a constant (which is known as Euler's number and its value is approximately 2.718) and the limit formula of 'e' is lim ₙ→∞ (1 + (1/n)) n.We can do the differentiation of e 2x in … WebJun 25, 2015 · Note that if we define $$ f(x)=\sum_{k=0}^\infty\frac{x^k}{k!}\tag{1} $$ we get $$ \begin{align} f(x)f(y) &=\sum_{k=0}^\infty\frac{x^k}{k!}\sum_{j=0}^\infty\frac{y^j ...
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WebAug 8, 2024 · Explanation: Here , y = e−x Let, y = eu and u = − x ∴ dy du = eu and du dx = − 1 Using Chain Rule: dy dx = dy du ⋅ du dx ∴ dy dx = eu ×( −1) = −eu Subst, back u = − x ∴ dy dx = −e−x Answer link Jim G. Aug 8, 2024 −e−x Explanation: differentiate using the chain rule given y = f (g(x)) then dy dx = f '(g(x)) × g'(x) ← chain rule WebAug 8, 2024 · y = e−x. Let, y = eu and u = − x. ∴ dy du = eu and du dx = − 1. Using Chain Rule: dy dx = dy du ⋅ du dx. ∴ dy dx = eu ×( −1) = −eu. Subst, back u = − x. ∴ dy dx = −e−x. iowa leather weekend
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WebThe Derivative Calculator lets you calculate derivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. It helps you practice … WebLearn how to solve differential calculus problems step by step online. Find the derivative of 14x^2x13. The derivative of a function multiplied by a constant (14) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (x13) is equal to the constant times the derivative of the function. The power rule for … WebOct 3, 2024 · The derivative of e 4x is 4e 4x. Mathematically, we can write it as d/dx (e 4x) = 4e 4x or (e 4x )’ = 4e 4x. What is the derivative of e 4x? Answer: The derivative of e 4x is 4e 4x. Proof: By the logarithmic differentiation, we will find the derivative of e 4x. Let us assume that y = e 4x Taking logarithms with base e to both sides, we obtain that open book image outline