SVa' +x'dx- +x 2 +x' + C.

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: finf dy/dx by implicit differentiation when x^2=(3x+6y)/(3x-6y).

A: The given function is: x2=3x+6y3x-6y

Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

A:

Q: п/4 sec z dz

A: By using integration formula, we calculate the given integral.

Q: Explain the derivatives and integration.

A: Solution: Derivatives: Definition of derivatives is , the rate of change of a quantity with respect…

Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: Solve using variation OF patometert O reductian OF order CD-+)y= secx csc x csc X

A:

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

A:

Q: x³tanh² (x*) sech²(x*) dx

A:

Q: What’s the difference between differential and inferential Calculus? And How do they apply to…

A: DIFFERENCE BETWEEN INFERENTIAL AND DIFFERENTIAL CALCULUS:…

Q: tion of the tangent line to f(x) = 4 %3D

A:

Q: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: The total derivative of f(x,y) = ylnx  is

A:

Q: y = x* + 2 sin(x) + xº + 24*.

A:

Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: what is the partial derivative of 2=Yytylnlxy

A: Given query is to find the partial derivatives.

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: How would you find the stationary points of partial derivative equations coming from a multivariate…

A: Stationary points:

Q: tanx 4) S Edx Cosxv1+secr 5) S(1- u)vudu

A:

Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

A:

Q: can explain for me what is Applications of Partial Derivative ?

A:

Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

A:

Q: ди ди x====u+Yay ?х

A:

Q: Compute da -dx

A: ∫05e-xxdx

Q: Use implicit differentiation to find dy/dx in x2(x - y)2 = x2 - y2

A:

Q: Find both first partial derivative Z = 15x x/y az az ду

A: As we know that: The the Power law: ddxxn=nxn-1 From the given problem: z=15xy

Q: Find anti derivative 3x^2(y^2+1)

A:

Q: Find both first partial derivatives. az

A:

Q: How can you relate antiderivatives as an opposite of derivatives in your life?

A: Solution:   Antiderivatives are the inverse operations of derivatives or the backward operation…

Q: Calculate the partial derivative * using implicit differentiation of exy + sin (3xz) + 2y = 0. (Use…

A:

Q: Give 1 problem application of differential

A: We have to explain a real life example of differential equation.

Q: What

A: The correct option is (B).

Q: Find the first and second order derivative w=3z7-7z3+21z2

A:

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Determine the derivative of y. y = eV14x+6 %3D

A: Please refer the attached image for complete solution.

Q: How do you find the partial derivative of a given function using the definition formula?

A:

Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

A:

Q: 5z²)* 4/3 %3D

A: (3). The function is given by Hz = 1-5z243 To evaluate: The derivative of the function.

Q: Calculate Calculate 1 f (425 - / +6²-8) dz 4x - dx. X S 5² - -x³√x² + 3 dx 3 ln³ Calculate 41³ (2)…

A:

Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Use linear approximation or differentials to estimate v80. Show your work.

A:

Q: J7 -dz 21-8

A:

Q: i Explain. Reducible the working procedure of Equation to Homogencous. form.

A: Given: Procedure of equation Reducible to Homogeneous form.

Q: How can you apply integral and differential calculus in real life situations?

A:

Q: dy by implicit differentiation of 2r2 3y2 = 4?

A: