Find the derivative of y = arctan(1 + e²x). О 1 yl= 1+(1+e²)² О 1+e2x yl= ○ yl= 1+(1+e²x)² e2x 2 1+(1+e²*)² 2 О yl= 2e2x 2x 2 ,

Q: Evaluate y' y = cosh²12x +sinh²6x

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Q: ind f'(x). f(x) = ln(cos5(3x4))

A: topic:- derivatives

Q: If x = t^2 + 1 and y = t^3, then the second derivative is? (Show your complete solution). a. 3/(4t)…

A: Given that,   x=t2+1 and y=t3

Q: Find f'(z) of f(z) = e(z^3) - 5z.

A: Given :- f(z) = e(z^3) - 5z

Q: Find h' (2) if h(x) = 1n(x + √(x2 - 1)) h'(2) =

A: Given hx=lnx+x2-1

Q: 19. e* +e" = e*+ 20. ye* +xe" =1

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Q: Find the derivative of the following: y = 2x* + + 3a? – 7 O y' = 8x³ + a² + 6x O y' = 8x + 2æ² + 6x…

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Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

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Q: Find the | y' = 12x³ – 12x² – 12 Oy' = 6x² + 6x Oy' = 6x² - 6x Oy' = 12x + 6 derivative if y = 2x³ +…

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Q: 4. f(t) = (e^(10t)) sin(2t) 5. f(t) = (e^(9t)) sinh(5t)

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Q: if x=t^2+1 and y=t^3, then the second derivative is?

A: x=t^2+1⇒dx /dt​=2ty=t^3⇒dy/dt = 3t^2​

Q: Find the derivative of the funcion. y=x-17 +63x+6

A: y = x3-17x2+63x+6 y'=dydx=ddxx3-17x2+63x+6 Here we are gonna use the formula  ddxxn=nxn-1

Q: Suppose that f(4) = 2 and f' (4) = h(x) = (2x² + 3in (f(x)))² h' (4) = (b) h(x) = 20f(x) e-2x + 3…

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Q: Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.

A: Given differential equation     x2y'=y   and initial condition  at x=1,y=2/e

Q: Solve (e' +1) cos x dx +e'sinxdy = 0

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Q: у 3 1og(3 - 4x + х')

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Q: Give a negative rotation that defines the angle π /3.

A: Given: A negative rotation that the angle π3

Q: Consider sec(7x+y)=e^7x Determine the derivative of y with respect to x. y' =

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