Differentiate: y=ln(x)/x^8 dy/dx=

Q: find y' for y = 2Vsinx sinh-1(logx). %3D

A: y'=log2· 2sinx-1.cosx.sinh-1(logx)sinx+2sinxxlog2x+1

Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

Q: 11. y=3x+ ln x %3D

A: Topic - derivatives

Q: Find the derivative of the function y = ln(tanh x/2)

A:

Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: dx

A:

Q: Integrate O sinh 2x dx

A:

Q: Differentiate  y=sin(ln(5x2-2x))

A:

Q: 4 x ) dx. 4 tan x

A: topic - definite integral using integration properties

Q: Differentiate y =( logx) sinx

A:

Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: Find the derivative. Simplify where possible  y = cosh (ln x)

A:

Q: Differentiate with respect to the independent variable: y=tan[ln(3x2+5)]

A:

Q: 1) [(sinh 2x + cosh2x)° dx

A:

Q: (A) Ln(2) S Sinh(x) Cosh² (x) dx

A:

Q: dy Use logarithmic differentiation to find dx y = (sin(2x))9x dy (sin(2r)) *(18x cot(2x) + 7…

A: Question is solved.

Q: 5th derivative of y = log x^5 to the base 2

A:

Q: dx х V1-4 ln?х

A:

Q: calculate the derivative. y = sinh x tanh x

A:

Q: Integrate tan -1 x dx without using integration by parts.

A: We will find the solution in the following step.

Q: Find dy/dx by implicit differentiation. csc x = x(1 + tan y)

A:

Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

A:

Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

Q: Calculate the derivative. 1 y = log 5x y' =0

A:

Q: 3. x)dx sin(ln

A:

Q: dx

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: implicit derivative to find dy/dx of    xy + arcsin(y)+2^y=ln(x)

A:

Q: Find intregal indefinite dx =

A: To evaluate the given indefinite integral.

Q: Find dy ldx by Tmplicit differentiation. tanLx-y)=

A:

Q: Find the indefinite integral. ∫ sinhx / (1 + sinh2x) dx

A:

Q: Find the derivative of y(x) = In (9(ln(x))’). (Use symbolic notation and fractions where needed.) dy…

A: To find the derivative of yx=ln9lnx7.

Q: Integrate ∫(ln(x))/x

A: We need to integrate the given logarithm function:

Q: Integrate: dx

A: By substitution method, integration of function is solved step by step .

Q: sin“ (x)dx 4

A:

Q: Integrate: S dx

A:

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Differentiate the function. y=ln(x5sin2x)

A: Given function:

Q: tanh 2x In (cosh 2x)dx

A:

Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

Q: calculate the integral.

A:

Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: Without integrating, explain why

A: when the integration is in the form  ∫-aaf(-x)=∫-aa-f(x) is odd then it is equal to 0

Q: 2 cosh x+sinhx

A:

Q: Integrate completely

A: Given,             ∫2x+12x-53dx

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

A:

Q: Se Sin (3x) dx by Improper htegrations.

A: use improper integral

Q: Find the integral ∫dx / sinhx+2coshx.

A: Given Data The integral is ꭍdx/sinhx+2coshx.   Using the Weierstrass substitution in the given…