find the derivative of the fuction f(x)= 5sinx/3x+cosx

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

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Find the derivative of f(x) = sin x²+ cos x if f'(2)

A: Given function is fx=sinx2+cosx. It is differentiated as follows by using the sum rule of…

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: Find the derivative of the function. y = x°cos x - 10x sin x - 10 cos x

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Q: Find the derivative of f(x) = 3x° cos(x). 8 CoS f'(x)

A: Given query is to find the derivative of the function.

Q: Find the derivative of the function y = 2x sinh−1(2x) − √(1 + 4x2)

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Q: Find the derivative of the function. 1 + x 1 - x y = arctan y' =

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Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 x - x sech-1 x

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Q: find the derivative using the appropriate rule or combination of rules. y = (x3 + cos x)−4

A: Given that, y=(x3+cosx)-4

Q: Find the derivative of y with respect to x 3tan-1x + sin-1x = 4

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Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: Find the derivative of f(x) = 2(x² + 3x) cos(sin(x³)).

A: I have used product re and derived of composition of two function

Q: Find the derivative of f(x)=arctan(1/x) and simplify

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Q: Compute the derivative using derivative rules. y = tan(x 2 + 4x)

A: We have to compute the derivative of the function: y=tan x2+4x We know the formula of derivatives,…

Q: Calculate the derivative of the function y=1+cosxsinx.

A: Given: y=1+cosxsinx we know that for finding derivative of given function we need to use product…

Q: Find the derivative using the appropriate rule or combination of rules. y = x cos(1 − 3x)

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Q: Find the most general anti-derivative of f(x) = 9Vx +1+ cos x.

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Q: cosx y =-

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Q: Compute the derivative using derivative rules. y= cos(1/x) / (1 +x 2)

A: Derivative: The rate of change of a function with respect to a variable. y=fxy'=limh→∞ f(x+h)-f(x)h

Q: Find the derivative of the function y = 2x arccos x − 2√(1 − x2 )

A: If the two functions f(x) and g(x) are differentiable (the derivative exist) then the product is…

Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =

A: h(x)=x2tan-1(x)

Q: find the derivative of y with respect to the appropriatevariable. = cosh-1 2√x + 1

A: Given: y=cosh-12x+1Here ,we havecoshy=2x+1Taking the derivatives on both…

Q: Find the derivative of the function .

A: Given a function f(x)=2x3+3 cos x f(x)=2(x)1/3+3 cos x      =2x-1/3+3 cos x We, use the following…

Q: sinx (b) у %3D V1+cosx

A:

Q: Find the derivative using the appropriate rule or combination of rules. y = (x3 + cos x)−4

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Q: Find the derivative of the function y= arctan x +x/1+x2

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Q: Find the derivative of the function by using the chain rule. sinx (a) h(x) = tan(x³ sinx) (b) y= %3D…

A: To find the derivative of the given function using the chain rule, which is:…

Q: Find the derivative of f(x)= (x^2)sinx

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Q: Find the derivative of f(x) = sin x²+ cos x

A: fx=sinx2+cosx

Q: find the derivative of y with respect to the appropriatevariable. y = (x2 + 1) sech (ln x)

A: Given: y=x2+1sechlnx

Q: h(x) = tan(x' sinx) sinx (b) y= - V1+ cosx

A: Topic = Derivative

Q: Can you help me step by step?

A: To differentiate the given expression y=f(x)

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 y with respect to x. y= ln3x

A: We can solve the given problem using chain rule derivative.

Q: Find the derivative of the function y = 2x − cosh √x

A: The given function is y=2x-cosh x. Obtain the derivative of y=2x-cosh x as follows.

Q: (a) h(x) = tan(r'sinx

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Q: Find the derivative of the function. 10 f(x) = + 6cos x Vx

A: Differentiate above equation with respect to x

Q: Find the derivative of: x²y = (y + 2) + ry sin(x)

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Q: Find the derivative of y = 2x cos x − 2 sin x.

A: Given function y=2xcosx-2sinx dydx=ddx2xcosx-2sinx=ddx2xcosx-ddx2sinx Recall the formula…

Q: Find the derivative of the function y = x tanh−1 x + ln√(1 − x2)

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Q: Find the derivative of f(x)=(sinxcosx)1/2

A: Given the function,

Q: sinx (a) h(x) = tan(x² sin.x) (b) y= V1+cos.x

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

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Q: Find the derivative of y with respect to x. y=ln(tan-1(4x5))

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Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 x/2

A: We have to find derivative of y with respect to the appropriate variable: y=cosec-1x2 Rewriting the…

Q: 2.) y = tan¬1 – 6•x³ y' =

A: We have to find the derivative of the function: y=tan-1-6·x3 We know the formula of derivatives,…

Q: Obtain the derivative of the function y cos (9y ) + tan (4x) csc (2x) y =

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Q: r(x)= cos (3x)

A: