Differentiate the following functions using appropriate differentiatio f(x) = (x² + cos x)10 f(x) = sin(3x? + 2x – 1) f(x) = e3x²+5x-1 f(x) = V2x – 5+ ex f(x) = sin (2x2 + 1) f(x) = (5x + 1) (7x – 5)8 f(x) = 52x²-t | %3D -
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A: Here I am attaching image so that you understand each and every step.
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Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)
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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Find the derivative of f ( x ) = 6 sin ^2 ( x ) + 6 cos^2 ( x ) at x = -6.5Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y = cos h-1 √2x 3. y = tan h-1 (2 / x)
- A. Determine the correct value of the derivative at x=2. B. Use the best numerical differentiation method of 2 points to take the derivative of 2.How do I find the 20th derivative of f(x)=(2cos x)(cos 3x)? I think there must be some trick because this was on a timed test with about 40 questions.Find the 2nd derivative of y with respect to x.In y = 2^x+cosh^-1 (2x)
- Find the first derivative of y = cos4 x – sin4 x y = x3 – x2 cos x + 2x sin x + 2 cos x y = (x – 1) √ (2x – x2) + arcsin (x – 1) y = arctan [ (3 sin x) / (4 + 5 cos x) ] y = ( ex – e –x ) / (ex + e –x ) y = ln [ x + √ (x2 + 1) ] Simplify the answer.Find all relative extrema of the function f(x) = x^4 − 4x^2 + 2 by using the Second Derivative test where applicableFind the derivative of f(x). f(x)=(x^2)(sin^2(2x^2)) Apparently the answer should be 2x(sin^2(2x^2))+(8x^3)(sin(2x^2))(cos(2x^2) I keep getting 4x^3 instead of 8x^3 and I don't know where the 8 comes from.
- (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this equation to obtain f' (x) + g' (x) = 0. This implies f'(x) = -g'(x). (b) f' (x) = 2 sin x cos x, and g'(x) = 2(cosx)(-sinx) = -2sin x cos x. So, f'(x) = -g'(x).Find the derivative of the function using implicit differentiation. 1.) x²y + y²x = -2 2.) √(xy) = x²y+1 Find the antiderivatives for integral notation. 1. (x+7) dxFind the derivative of each function by using an appropriate differentiation rule. 1) f(x)=3x^3 - 4e^(-x^2) + ((5)/(4x^3)) 2) g(x)= x^4 tan^(-1) (x^5) Recall that tan^(-1)x=arctan(x) 3) h(x)= e^(-2x) cos x