Find the first derivative of y=x² O a. y' = r²lnz O b. y'= -2² (1+ Inz) y'=r(1-Inz) °c O d. none of these Oe. y'=(1+ Inc)

Q: Find the indicated nth derivative of the following: 8. 25th derivative of y = sinh8x ans. y25) = 825…

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Show that cosh r d tanh-(sinh r) dr %3D 2 – cosh?(r) Show that the derivative of y = x* inh= is…

A: Please find the detailed proof.

Q: .3 Find the derivative of the function f(s)= 12s³+ 5secs. a. f'(s)=36s² + 5secs · tans b. f'(s)= 3s²…

A: We have to find derivative

Q: 10. Find the first derivative of sin (y) + cos (x) = 1. cosx siny sinx a. y' b. y' %3D cosy C. y'…

A: We have to find the first derivative of sin(y)+cos(x)=1.To find the derivative we use chain rule of…

Q: Find the first derivative: y= ln v5x3 –- 2 5, O y = 222 %3D 523-2 O y' = 322 5z3-2 O y' = 622 5z3-2…

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Q: f(1) = F + а. b. g(x)=In(x)e3r с. А(0)- sinh (0.50) k (x) = 2.x +1 x² - 2 d.

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Q: r(t) = ( tan(7t), sec(8t), -'(t) =

A: rt=tan(7t),sec(8t),1t2 We have to find r'(t)

Q: State the order of the given ordinary differential equation, and classify it as linear or…

A: Given: d. d5qdp5tan2q=p2q-qsin(p)eap e. -9sinh(at)=z'''-az't-2 f. r''=-a5x+rsinrx g.…

Q: If f(x) = sin² x, find f'(x) f'(x) = Find f'(2) f'(2) =

A: Given that the function fx=sin2x. Find the derivative f'x and f'2.           The formula used is the…

Q: 1 ["Co 0 Approximate e cos x dx using 0 P₂(x) dx OA. 1.75 OB. 1.25 O c. 1.125 O D. 1.5

A: Sol:- First find P2xA Maclaurin series is given byf(x)=∑k=0∞f(k)(a)k!xkIn our case,…

Q: 4 Vx. 7 Vx, What is the derivative of y ( In 7 + In 4 ) 28 Vx (A) y' = ( In 11 ) 28 Vx y' 2 X 7 In…

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Q: You want to differentiate Y = E coe) so you take the the natural log of both sides, first. What is…

A: Consider the function y=lny.

Q: If f(x) = sin(x³), find f'(x) Find f'(1)

A: See this solution in below.

Q: The integrating factor (IF) of the equation y' - 2ycot2x O A. sin2x O B. cot2x O C. Lnsin2x…

A: Solution:  To find the integrating factor of the given differential equations

Q: xy' +by = 0

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Q: (2x+3)5

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Q: 2. Let h'(2) = 8, h' (2) = 5, h(2) = 3, h″(4) = −—1,h'(4) 4 ª[₂x x.h"(x) dx. 3, h(4) 6. Find = =

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Q: 18. Find dy/dx by implicit differentiation.

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Q: 14. Find the second derivative of tanh xy + xy =0 by implicit differentiation. A. y" =2 B. y" =2 C.…

A: Answer is option C)  y''=2y/(x^2)

Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

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Q: Question If y(x) = In 4x²+5x+4 5 x 6 tan x find y'(x).

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Q: The first derivative of a continuous function y = f(x) is y' = (6x - 5x²) (3 − x)². Find y' and then…

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Q: Find y' and y". y = x² In(9x) y' = x + 2x ln (9x) y" = 3+2 ln( 9x)

A: Given function is Differentiating with respect to x by using product rule of differentiation, we…

Q: Find the following antiderivatives. a. ∫(3x^4-cosx)dx b. ∫(5^3sqrt(x^2) + 2x-1)dx c.…

A: ∫xn dx = xn+1n+1+C. ∫ax dx = axloga+C

Q: Find the anti-derivative of

A: Answer and explanation is given below

Q: 6. y = In (e* + e") 7. y = tan e + etanax 8. y = In(x + Vř +1) 9 y = Arctan(;

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Q: 3. What is the FIRST derivative of the given function? y = 3x³ - 2x² + x - √√2

A: Given,            y=3x3-2x2+x-2To find : What is the first derivative of the given function.

Q: dy y'= 3r?y = dx Up to y''only. For 0sxs2; y(0) = -1;h=0.1

A: Given y'=3x2y2     (1) Differentiating with respect to x, we get y''=6xy2+6x2yy' from (1)…

Q: If h (z)=3-2x+5 ln (z+4) then determine h' (1). h' (1) = Number

A: h(x)=3-2x+5lnx+4d dx(xn)=nxn-1d dx(constnat)=0d dx(lnx)=1x

Q: 15. sin x + cos y = sin x cos y

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