Use forward and backward difference formula with h = 0.1 to approximate the derivative of f(x) = In(x) at x = 1.8

Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: Find the derivative of the function f(x) = (In x)°.

A: Given that,             f(x) = lnx3 Differentiating with respect to x, we get                  f'(x)…

Q: Find the derivative of function.

A: Find the derivative of function. y=(ln|x+1|)4

Q: Find the 7th derivative of: f(x)=sin(x)cos(x) f’=? • • •

A:

Q: Find the derivative. g(x) = tanh-1(x?)

A:

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: g(x) = In tanh-1 x

A:

Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: Derive the formula for the derivative with respect to x of csc x.

A: We will write cscx= 1/sinx  Then we will use the quotient rule to differentiate

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A: Given function is y=ex-12. To find the derivative of the given function. Solution: Chain rule of…

Q: Find the derivative of each function at the specified value of x.

A: We have to find the derivative of the function at the given value of x: gx=ex sinπx, when x=0. We…

Q: Determine the derivative of f(x)=ln(x√x^2+1).

A:

Q: 4. Find the 2nd derivative of f(x)=14-x (x)%3D

A: The give function is fx=4-x

Q: f (x) = ln(x · 5*)

A:

Q: Find the derivative of f(x) = ln∣cos x∣.

A:

Q: Find the derivative of the functions. y=cosh^-1 (3x)

A: We have to find derivative of the function: y=cosh-13x Rewriting the function, y=cosh-13xcosh y=3x…

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: Use three-point midpoint formula to evaluate the first derivative of y=tan(x) at x = O-2√/2 00…

A: Given function is y=tanx. We have to evaluate the first derivative of y=tanx at x=π4 using a value…

Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

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Q: Find the second derivative of g(x) = sinh(x) cosh(x)

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Q: 3/x +1 f(x) = X+2 at x = -1

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A:

Q: Use forward-difference formula to evaluate the first derivative of y = tan(r) at a = using a value…

A: We know that the forward difference formula is: f'(x)=f(x+h)-f(x)hThe given function is : y=tan(x)We…

Q: Find the derivative of the function.

A:

Q: State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the…

A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: Find the first derivative of the function of f(x) using any method?

A: Given,

Q: Use the chain rule and product rule to find the derivative of f (x) = e" (sin(x)² + x).

A: Given Data: Function: ex(sin(x)2+x)   The chain rule of the derivative is, ddxfgx=fgxg'x ......1…

Q: Find the derivative of the function.   y = In(x)/x9

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log25 ex - log5 √x

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Q: Find the 2nd derivative of the given function fCt) = t² Int

A:

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: Use high-accuracy differentiation formula O(h) to estimate the first derivative of f(x)=log.x.…

A: Consider the given function, fx=logx Here we need to estimate the first derivative of the given…

Q: What is the first derivative of g(x) = ln #*+1? x2

A: Derivative of ln(x):       ddx(ln(x))=1x Division rule of derivative:-…

Q: Use Delta method to find the derivative of e*

A:

Q: the derivative of f(x) = xi at the point x = 4?

A:

Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

A:

Q: Find the derivative of the function y using the increment method or three- step rule. vx +1

A:

Q: Obtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h =…

A: Given  f(x) = sinxx we have to obtained the first derivative of f(x) by using  Richardson's…

Q: Find the second derivative of g(x) = secx.

A: Given : gx = sec2x

Q: Find the second derivative of y=x-1 at x=2

A:

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

Q: 4. Find the 2nd derivative of f (x) = 4-x x)%3)

A: To determine the second derivative of the function given by; f(x)=4-x Differentiate the function…

Q: State the notation/symbol for: derivative of y with respect to x derivative of f(x) second…

A: Since you have asked multiple questions in a single request, we would be answering only the first…