WebJul 8, 2015 · Modified 7 years, 8 months ago. Viewed 519 times. 1. y = e − 4 x sin 5 x. My answer is: y ′ = e − 4 x ( cos 5 x) ( 5) + ( sin 5 x) e − 4 x =. e − 4 x ( ( cos 5 x) ( 5) + ( sin … WebCalculus. Find the Integral 4e^x. 4ex 4 e x. Since 4 4 is constant with respect to x x, move 4 4 out of the integral. 4∫ exdx 4 ∫ e x d x. The integral of ex e x with respect to x x is ex e x. 4(ex + C) 4 ( e x + C) Simplify. 4ex + C 4 e x + C.
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WebSolution: Derivative Steps of: ∂/∂x (4x^2 + 8xy + 2y) Multivariable critical point calculator differentiates 4x^2 + 8xy + 2y term by term: The critical points calculator applies the power rule: x^2 goes to 2x. So, the derivative is: 8x. Again, the critical number calculator applies the power rule: x goes to 1. The derivative of 8xy is: 8y. WebCalculus Find the Derivative f (x)=-4e^ (-5x) f (x) = −4e−5x f ( x) = - 4 e - 5 x Since −4 - 4 is constant with respect to x x, the derivative of −4e−5x - 4 e - 5 x with respect to x x is −4 … north austin news
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WebAug 10, 2024 · f (x)=e^x : this will be our original equation that we want to differentiate to achieve the general formula. As noted by this video, the general formula for this equation is the equation itself: e^x. Let's prove it using the general limit notation! First, plug in (x) and … WebThis is sometimes called the sum rulefor derivatives. EXAMPLE3.2.1 Find the derivative of f(x) = x5 +5x2. We have to invoke linearity twice here: f′(x) = d dx (x5 + 5x2) = d dx x5 + d dx (5x2) = 5x4 + 5 d dx (x2) = 5x4 +5·2x1 = 5x4 + 10x. Because it is so easy with a little practice, we can usually combine all uses of linearity into a single ... WebCalculus. Find the Critical Points f (x)=x^4e^ (-5x) f (x) = x4e−5x f ( x) = x 4 e - 5 x. Find the first derivative. Tap for more steps... −5x4e−5x +4x3e−5x - 5 x 4 e - 5 x + 4 x 3 e - 5 x. … north austin medical center rehab