WebCalculate the derivative d x d ∫ x 6 e 12 x ln (t) d t using Part 2 of the Fundamental Theorem of Calculus. Enclose arguments of functions in parentheses. For example, sin (2 x). d x d ∫ x 6 e 12 x ln (t) d t = WebFind the derivative of f (x) = 2x Solution We write 2x= ex ln 2 Now use the chain rule f '(x) = (exln 2)(ln 2) = 2xln 2 LogsWith Other Bases We define logarithms with other bases by the change of base formula. Definition ln x logax= ln a Remark: The nice part of this formula

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WebLet g(x, y, z) = sin(xyz). (a) Compute the gradient Vg(1, 0, π/2). (b) Compute the directional derivative Dug(1, 0, π/2) where u = (1/√2,0, 1/√2). (c) Find all the directions u for which the directional derivative Dug(π, 0, π/2) is zero. ... (t)=ln(13/t+1)4/t Minimum … Webderivative\:of\:\frac {\ln (4x)} {4x} \lim_ {x\to\:0} (\frac {e^ {-2x}-1} {x}) \frac {d^ {2}} {dx^ … how many amps does a 5000 btu window ac use

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WebDerivatives of logarithmic functions are mainly based on the chain rule. However, we can generalize it for any differentiable function with a logarithmic function. The differentiation of log is only under the base e, e, but we can differentiate under other bases, too. Contents Derivative of \ln {x} lnx Derivative of \log_ {a}x loga x WebFind the derivative of the function. \[ f_{(x)}=x^{2} e^{x}-2 \ln x+\left(x^{2}+1\right)^{3} \] … WebJul 19, 2024 · dy dt = 2t −1 t2 +4 Explanation: Given that y = ln(t2 + 4) − 1 2tan−1( t 2) differentiating above function w.r.t. t using chain rule as follows dy dt = d dt (ln(t2 +4) − 1 2tan−1( t 2)) = 1 t2 + 4 d dt (t2 +4) − 1 2 1 1 +( t 2)2 d dt ( t 2) = 1 t2 + 4 (2t) − 1 2 4 t2 +4 ( 1 2) = 2t t2 + 4 − 1 t2 + 4 = 2t − 1 t2 +4 Answer link how many amps does a 60 hp motor draw