(a) x' = 5t²x³ (b) x' + tsinx=0 (c) x"" = 5t²x³

Q: (In(x))? x3 dx /1

A:

Q: f'(x) = ƒ'(e¹) = f(x) = -3x² Inx

A:

Q: F(x) = L [~ 3 (542)

A:

Q: P(t)= 952e^(0.12)t Solve for t when P=20,000

A:

Q: How does (1/ln10)((-10^z)/(ln10)) become -1/((10^z)(ln10)^2)?

A:

Q: let f(x)=(ln x)^7 f '(x)= f'(e2)=

A:

Q: If y = x * ln(x) Then, y' + ∫y dx - (1/2)xy = ? a) ln(x) - (1/4)x2 + C b) x * ln(x) + C c) x + C…

A:

Q: Find g' (e) if g(x) = In(2x + e³).

A:

Q: eu [(= + e (+ + e" Inu - e" ln x) du

A: integration

Q: How would I calculate the principle value of  ln(-ie)

A: Given, z=lne-i Convert e-i to polar form. For a complex number a+bi  polar form is given by,…

Q: does ln(inf)/(inf)=0

A: the statement is false see below the explanation

Q: ln[(x^(2)-x-6) /  ((x+7)^(3))] ^ ((1)/(5))  =  ?

A:

Q: If f(x) = 4 In(8 + a), f'(x) = a + 8 f'(4) =

A:

Q: 1/2ln(4x^4)-ln(2)=6  solve for x

A: Given ln(4x4)2-ln(2)=6 as we know alnx=ln(xa)lna-lnb=lnablna=b⇒a=eb

Q: g(x)=(4x^2-5x+1)e^x g'(x)=

A:

Q: If f(x) = 5x² ln(6x), then f’(x) = f'(x)= f’’’(æ) = f (*) (2) = f(5)(2) =

A: Please see the answer below.

Q: 2hv3 1+ In-1 I,c²

A: Let's find.

Q: Given h(x) = 4x^6sec(lnx), find h'(x)

A: GIVEN h(x)=4x6sec(lnx)   TO FIND h'(x)=?

Q: 二十三 _{{x} = {\}\

A: Assume the bracket part as another variable and then use Chain Rule. And use basic identities of…

Q: Find f''(x) f(x)=3x^2-13x-4/x^4

A: Given Find f''(x) f(x)=3x^2-13x-4/x^4

Q: f F(x)= 8x^2 ln(6x) Than, F'''''(x)=

A: Given that F(x)=8x2ln6x find F’’’’’(x)

Q: Si f(x) = (x2) / (1+x). Calcule f''(1).

A:

Q: n x” lnxdx X

A: Given that

Q: f(x) = (2x2 – 5x)ln(x² – x) f'(x) = ?

A: Product Rule ddx(h(x)g(x))=ddx(h(x))g(x)+h(x)ddx(g(x)) Chain Rule ddx(h(g(x)))=ddhu(h(u))ddx(g(x))…