Differentiate. f(x) = x2 sin(x) f'(x) =

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

Q: (5x) S sin(x) tan(x) .........

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Q: 2. Find the derivative of y = 2 1 1- x² + arcsin x 2

A: As per our guidelines, I can answer only one question and maximum three subparts of a question.…

Q: Determine the derivative of f(x) = Cosh(5 x) csc(x)

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Q: 2. y = (cosx)(sin5x)

A: We will use product rule of differentiation to find the first derivative of this function. We will…

Q: find the derivative  f(x)=cosx/1+sinx

A: The derivative of the function as follows.

Q: Va2 -x2 y=Arcsin + 6. X

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Q: sin

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Q: 1. Find the derivative of f(x) = tan³(sinx) + %3D

A: The given function isf(x)=tan3(sinx)+x3+3x4

Q: 3- Find the derivative of sinx +x /2+cos x.

A: The given function is fx=sinx+x2+cosx. The formula for differentiation for the sum of functions is…

Q: Compute the derivative. (x) = ex sinx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative of f(x) = tan³(sinx) + +

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Q: find the derivative of the function by the Logarithmic differentiation method.   y=(cos(x))ln(x)

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Q: What is the derivative of 2(x)ln(x)+x

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Q: Compute the derivative of the function y = 7 sin¬'(x) at the point x = (Use symbolic notation and…

A: A detailed solution is given below

Q: Show that (x ln(x)) ‘ = 1 + ln(x) using the Product Rule for Differentiation.

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Q: 3. Find the derivative of f (x) = 2x²e² tan x.

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Q: 2. Use logarithmic differentiation to find first derivative of y = (sinx)*

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Q: what is the differentiate of f(x)=ln x

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Q: Use logarithmic differentiation to find the derivative of the function. y = (sin 3x)In x sin()…

A: Formula used:If (x) and g(x) are two differentiable functions, then following rules  are efined as;

Q: Find the 139th derivative of y=cos x а. Cos x b. Sin x С. -Cos x d. -Sin x

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Q: What is the derivative of ln(sin x + cos x)

A: Consider the given function:

Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: compute the derivative f (x) = ln(csc−1 x)

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Q: Find the derivative of the function. h(x) CoS x 6. %3D 1+ sin x sin x -61 coSX --6 cosx (1+ sin x)6…

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Q: How do you use implicit differentiation to solve:  tanxy=x+y   at point (0,0)

A: The given expression is,

Q: Compute the derivative of the function y = 8 sin-(x) at the point x = (Use symbolic notation and…

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Q: Use Leibnitz's Theorem to calculate the 4th derivative of y = x^sin (3x)

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Q: find the derivative of this inverse hyperbolic function f(x) = cosx tanh-1(sinx)

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Q: FIND THE FIRST DERIVATIVE OF THE FUNCTION cos r. y = cosx О а. SIN3X O b. - COS3X О с. COS3X O d.…

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Q: cos X sin x + cosX

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

A: Applying natural logarithm on both sides, we get

Q: Compute the derivative of the function y = 6 cos- (4x) at the point x = (Use symbolic notation and…

A: Solution ) y = 6 cos-14x Differentiate with respect to x  y' = 6 d/dx (cos-14x) [ we know that  d/dx…

Q: Find the derivative of the function. using chain rule y = sin(sin(sin x))

A: Given: y=sinsinsinx

Q: 3. Find the second derivative using implicit differentiation x² + y? = 4

A: Given that x2+y2=4To find implicit differentiation

Q: Va2-x² Y=Arc sin + a

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Q: Find the first derivative of 1 2 y -sin?

A: Explained below

Q: Use Leibnitz's Theorem to calculate the 4th derivative of y = x+sin(4x)

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Q: f(x)= sinx/cos x+1

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Q: Find the derivative of: sin sin(2x) sin sin(x) + cos (2x) cos(x) ans: -sinx solution?

A: We will use the formula cosA*cosB+sinA*sinB= cos(A-B) , with A=2x and B=x and simplify.

Q: Solve for derivative. y = (x + cos x) ( 1 - sin x)

A: Given          y = (x + cos x) ( 1 - sin x)

Q: Compute the derivative of the function y = 5 sin-'(x) at the point x (Use symbolic notation and…

A: We know, ddxsin-1(x)=11-x2

Q: 3rd derivative of y sin 3x

A: Here we have to find the 3rd derivative of           y = -1/sin(3x)

Q: Find the derivative of  f(x) = sin(arcsin x) / arctanx

A: Let u=sin(arcsinx)u'=cos(arcsinx)ddx(arcsinx)u'=cos(arcsinx)11-x2u'=cos(arcsinx)1-x2Let…

Q: derivative

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Q: Find the first derivative of the function below: f(x) = arctan(sec(x ))

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Q: second order derivative of (5 sin 3x+cos^2 (3x )) is *

A: The function: y=5 sin3x+cos23x

Q: First Derivative of: (tan3(2x)) / x1/5 + ln(7x+4)

A: (U/V)' = (VU' - UV')/V^2

Q: 3 sin(x) +x² In(x) – 2x Find the derivative of f(x) = using derivative rules.

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Q: 1. 1. f(x) = 4x³ · cos x

A: Given: fx=4x3.cosx