Differentiate sin x 2 + x w.r.t. x
WebMar 30, 2024 · Ex 5.5, 4 Differentiate the functions in, 𝑥^𝑥 – 2^sin𝑥 Let 𝑦=𝑥^𝑥 – 2^sin𝑥 Let 𝑢=𝑥^𝑥 , 𝑣=2^sin𝑥 𝑦= 𝑢−𝑣 Differentiating both sides 𝑤.𝑟.𝑡.𝑥. 𝑑𝑦/𝑑𝑥 = 𝑑 (𝑢 − 𝑣)/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 𝑑𝑢/𝑑𝑥 − 𝑑𝑣/𝑑𝑥 Calculating 𝒅𝒖/𝒅𝒙 𝑢=𝑥^𝑥 Taking log both … WebMay 24, 2024 · Differentiate `sin^ (-1) ( (2x)/ (1+x^ (2)))` w. r. t. `tan^ (-1)x, -1 lt x lt 1`. Show more Show more License Creative Commons Attribution license (reuse allowed) …
Differentiate sin x 2 + x w.r.t. x
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WebJun 3, 2015 · Use the division's derivative formula: For a given function g: g = u v for u and v ≠ 0 other functions, the derivative of g is found as; g' = u'v − uv' v2 If we apply it to our case: f '(x) = (sinx)'(1 +cosx) −sinx(1 + cosx)' (1 +cosx)2 = cosx(1 + cosx) + sinxsinx (1 +cosx)2 = cosx +cos2x + sin2x (1 +cosx)2 WebDerivatives. Derivatives measure the rate of change along a curve with respect to a given real or complex variable. Wolfram Alpha is a great resource for determining the differentiability of a function, as well as calculating the derivatives of trigonometric, logarithmic, exponential, polynomial and many other types of mathematical expressions.
WebDifferentiate the following w.r.t. x : Solution The function that is to be differentiated is, e sin − 1 x Differentiate the function. d ( e sin − 1 x ) = e sin − 1 x d ( sin − 1 x ) d ( e sin − 1 x ) = e sin − 1 x × 1 1 − x 2 d x d d x ( e sin − 1 x ) = e sin − 1 x 1 − x 2 WebDifferentiate sin 2 (sin −1 (x 2 )) w.r. to x Advertisement Remove all ads Solution Let y = sin 2 [sin –1 (x 2 )] = [sin {sin –1 (x 2 )}] 2 = (x 2) 2 ∴ y = x 4 Differentiating w. r. t. x, we …
WebDifferentiate each of the following functions: (a) Since f (x) = 5, f is a constant function; hence f ' (x) = 0. (b) With n = 15 in the power rule, f ' (x) = 15x 14 (c) Note that f (x) = x 1/2 . Hence, with n = 1/2 in the power rule, (d) Since f (x) = x -1, it follows from the power rule that f ' (x) = -x -2 = -1/x 2 Websin − 1 (x x), 0 ≤ x ≤ 1 \sin ^{-1}(x \sqrt{x}), 0 \leq x \leq 1 sin − 1 (x x ), 0 ≤ x ≤ 1 advanced math Verify Mean Value Theorem, if f ( x ) = x 2 − 4 x − 3 f(x)=x^2-4 x-3 f ( x ) = x 2 − 4 x − 3 in the interval [ a , b ] [a, b] [ a , b ] , where a = 1 a=1 a = 1 and b = 4 b=4 b = 4 .
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WebApr 15, 2016 · Let y = sin−1x, so siny = x and − π 2 ≤ y ≤ π 2 (by the definition of inverse sine). Now differentiate implicitly: cosy dy dx = 1, so. dy dx = 1 cosy. Because − π 2 ≤ y ≤ π 2, we know that cosy is positive. So we get: dy dx = 1 √1 − sin2y = 1 √1 − x2. (Recall from above siny = x .) heather graham roller skatesWebFind the derivative of sin 2 (x). Let, y = sin 2 x. Differentiate both sides w.r.t x using chain rule . d y d x = d d x sin 2 x = 2 sin x × d d x sin x ∵ d d x x n = n x n-1 = 2 sin x × cos … heather graham robes longuesWebOct 19, 2016 · take natural logarithms to both sides and simplify lny = lnxsinx ⇒ lny = sinxlnx differentiate both sides wrt x d dx (lny) = d dx (sinxlnx) using implicit differentiation on the LHS; product rule on RHS = 1 y dy dx = cosxlnx + sinx x ⇒ dy dx = y(cosxlnx + sinx x) substituting back for y dy dx = (xsinx)(cosxlnx + sinx x) Answer link movie factsWebMar 30, 2024 · Example 23 Differentiate sin (cos (𝑥2)) with respect to 𝑥 .Let 𝑦 = " " sin (cos 𝑥2) We need to find derivative of 𝑦 𝑤.𝑟.𝑡.𝑥 i.e. 𝑦^′ = (𝑠𝑖𝑛〖 (cos〖𝑥^2 〗 )〗 ) 𝑑𝑦/𝑑𝑥 = 𝑑 (𝑠𝑖𝑛〖 (cos〖𝑥^2 〗 )〗 )/𝑑𝑥 = cos (cos〖𝑥^2 〗 ) . 𝑑 (cos〖𝑥^2 〗 )/𝑑𝑥 = cos (cos〖𝑥^2 〗 ). (−sin〖𝑥^2 〗 ) . 𝑑 (𝑥^2 )/𝑑𝑥 = cos (cos〖𝑥^2 〗 ). (−sin〖𝑥^2 〗 ) . 2𝑥 = − 2x sin 𝒙^𝟐. cos (cos 𝒙^𝟐) … movie fabulous baker boys castWebSolution Verified by Toppr Let y= sin x. Now differentiating both sides with respect to x we get, dxdy= 2 sin x.2 xcos x or, dxdy= 4 sin xxcos x Was this answer helpful? 0 0 Similar … heather graham pozzessere personal lifeWebDifferentiating both sides with respect to x, we obtain ⇒ u1dxdu= dxd (x)×log(sinx)+x× dxd [log(sinx)] ⇒ dxdu=u[1.log(sinx)+x. sinx1. dxd (sinx)] ⇒ dxdu=(sinx) x[log(sinx)+ … movie facial hair stylesWebSolution for Let 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).… movie facing the enemy trailer