In the scenario of the derivative of a logarithmic function, determine the slope of the tangent line to the graph of the function Y = Ln (Sin X), at X = - 3

Q: Find the function whose derivative is 1-e2x

A:

Q: 3.) y = log2 – 6·x³

A: Explanation: Given that,  y=log2(-6x3)

Q: In the given equation as follows, find an equation of the tangent line to the graph of the function…

A: Given: y = log3x and the point (27, 3). To find: The equation of tangent line at the given point.

Q: Find the indicated derivative and simplify. [3x log x³] dx [3x log x³] = dx (Type an exact answer.)

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: What is the derivative of the natural logarithm function ln x? How does the domain of the derivative…

A: Given: fx=ln x To find: (a) The derivative of f(x)  (b) Compare the domain of the derivative with…

Q: Find the first derivative:  y=log1o 5x+3/5x-4

A:

Q: x+1

A: By using the formula you can solve the given problem as follows :

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: Find the derivative of the function g(x) = log3 √(1 − x)

A:

Q: 1 ソ= 1- x

A:

Q: Solve for the second derivative of the following implicit function

A: We can solve this as follows:

Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

Q: find the derivative of y with respect to the givenindependent variable.73.y = log2 5u…

A: we have to find the derivative of y with respect to the given independent variable. (73) y=log25u…

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) -1 1

A:

Q: Find the derivative of the given log(cot(1-x2))

A:

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

Q: Find an equation of the tangent line to the graph of the function  y = log3 x, at the given point…

A: y = log3 x

Q: Find an equation of the tangent line to the graph of the function y = log10 2x, at the given point…

A: Given:y=log10 2x  through the given point 5, 1Equation of tangent line:y-y1=mx-x1Slope:dydx=f'x=m

Q: What is the first derivative of q(x)=(3x)7x at x=2?  Enter an exact answer in terms of a natural…

A: When there is variables in exponent we should take log both side then differentiate. Here we use…

Q: Find the derivative of the function f(x) = log23√(2x + 1)

A: To find derivative of fx=log22x+13

Q: Find the derivative of the function. f(x) = 2x2 In 2x f (x)= 2x[1+2 log(2x)]

A: fx=2x2ln2x

Q: What is the Derivative of the function; y = log10(1 − 4 tan x)

A:

Q: 2. y=cot1-2x 3. y=log22x*

A:

Q: Calculate the derivative of the following function. y = log 11(x-11) d. dx log 11(x- 11) =

A:

Q: The third derivative of the function is y = log 2x3

A: We can find the answer as below

Q: y = log,(4x - 8x)

A:

Q: Calculate the derivative of the following function. y = 8 log 2 (x² - 3)

A: Given, To evaluate,

Q: Calculate the derivative and use logarithm rules to simplify   g(x) = ln((x^3 + 2x)(x+1)^10)

A:

Q: Find the derivative OF the exponential funchion y = In ( 5- e **) Please simplify it Further.

A: Consider the provided equation, y=ln5-e4x Find the derivative of the equation. Apply the chain rule…

Q: Calculate the derivative of the following function. y=2 log5 (x -3) 2 log5 (x-3) = (²-3) =] dx

A:

Q: calculate the derivative of the following function. [ln(x^8)]^3

A:

Q: The derivative of the function y = cos(x In 3) log3(sin x) is:

A: Given,            y=cosxln3log3sinxTo find : The derivative of the given function.

Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

A:

Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: Find the derivative of the function y = log5 √(x2 − 1 )

A: Here given function as y=log5x2-1 or y=log x2-1log 5 The power rule for derivatives is expressed as…

Q: What is the derivative of: log x/(x+1)

A:

Q: What is the derivative of (ln(3x))/x^6?

A: Let y = (ln(3x))/x6.The derivative of y is with respect to x as follows.

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) 1

A: Tangent to a curve is a line which just touches the curve and in some sense is parallel to the…

Q: Find the derivative of the logarithmic function. y = In Isec x + tan x|

A: We have to find the derivative

Q: Compute the derivative of the given function. log3 x f (x) = %3D cot x - 2x2

A:

Q: Find the derivative of the function

A: given h(x)=log3xx-12we have to find the derivative of the given function

Q: Find the derivative of f(x) Give answer in exponential notation with positive exponents

A:

Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below:…

A:

Q: 2x+3) 17. f(x) =- (x² +1)*

A: topic - logarithmic differentiation

Q: Find the derivatives of 20" log(tan x)

A:

Q: What is the derivative of log (x²)? ○ 2x-log(x²) 1 x² 2x O log(2x) O exp(2x)

A:

Q: Find the higher-order derivative. (4 log 2(x – 5)) dx2

A: Given, d2dx24 log2x-5

Q: Find an equation of the tangent line to the graph of (log æ)cosh(a-10) , x >1 at the point where x =…

A: Given equation is  y=log xcosh (x-10), x>1 at x=10

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

A: