dy 1) Find for each of the following functions: dx COS X a) y =. 3-x b) y=e"-u) and u=2x-6 y=e(1-u) 3 c) y= 4x sec (3x) 2) Find y" if y= 3x²-In (2x)–8

Q: Evaluate f x'V 1+4x² dx.

A: Consider the definite integral ∫01x21+4x2 dx to evaluate this, first evaluate the indefinite…

Q: y" – 9y = t° – t e + sin(3t)

A:

Q: 4. Find d?y/dx² for the following functions: b) y = cos*(sec² 3x)

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Q: 2) Find the derivatives of a) y = 7 - 6x-x² b) y - ³x 8 √x

A: Given :(a)y=7-6x-x2(b)y=-8x

Q: 3.) Given y=5* (2, 1)? which of the following shows the equation of the line tangent to y at the…

A: To find the equation of the tangent line to the curve   at the point .

Q: dy 5- dx for y = tan (3x) is equal to: b) sec (3x) a) 6x sec(3x) tan(3x) c) 6x sec (3x) 6- dx for y…

A:

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: Differentiate y = VIn x 2 Inx +1 A. 2(In x)2 3. Inx-1 3 (In x)2 2 Inx-1 C. 2(In x)2 13 1. D. 3) 2(In…

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Q: 5) Sketch the graph of each function a) y=2" +1 b) y=3*1

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Q: + 9y = sec 3x

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Q: Find y in terms of x. dy = x 2 + 5, curve passes through (0, 14) dx x3 A) y = + 5x 3 B y = x3 + 5x +…

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Q: L=2-36X, y'co) =5, and ylo)=S x)

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Q: 2) 3. | 24 ly-11 dy

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Q: IV. Implicit differentiation 1. xy + y? = 1, find y? 2. x²y – xy? + x² + y² = 0, find y' 3. x? – xy…

A: Given: 1.xy+y2=1 , 2. x2y-xy2+x2+y2=0 3. x2-xy+y2=3 4. x3y+xy2=3 and x=1

Q: dy 3) Using the function y=f(x)=x², state which of the following uses of the notation: dx d and are…

A:

Q: Find stationary points of y = cos (4nt)

A: given function is

Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

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Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

A:

Q: 03) (Answer only two ): 4- Find the distance between the curve ( y=x+4) & line 0=x-4)

A: According to our guideline we can't solve multiple questions. so please repost the question…

Q: How did he get the second derivative step by step and a clear line please 3 F(x) = 1+e siny x Fex)…

A: Let fx=1+e-xsin 4x

Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: