as a function of x when y =

Q: Let f(x)=x2 - 3 Use the definition of the derivative to find f1 and f11 Write answer in form of…

A:

Q: Find y as a function of x if y′′′+81y′=0, y(0)=0, y′(0)=−81, y′′(0)=−81. y(x)=

A: Given that,                    y''' + 81y'=0.......equation(1)                 y(0) =0,  y'(0) =-81,…

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

A:

Q: Find the derivative of the function. f(x) = ((x2 + 3)5 + x)2

A: We use the power rule and chain rule.

Q: Find y as a function of x if y" – 11y" + 28y = 0, y(0) = 1, y(0) = 5, y"(0) = 6. y(x)

A:

Q: If f is a function defined by the equation y = f(x), then xis called the _______variable, and y is…

A: If f is a function defined by the equation y = f(x), then xis called the _______variable, and y is…

Q: Find the derivatives of the functions in Exercise

A: Given: y=1+x2x34-x-3 To Find: The derivative of the given function

Q: Determine whether the equation xy - 5y = 1 defines y as a function of x.

A: Here we determine whether the equation xy-5y=1 defined y as a function of x.

Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

A:

Q: Find the derivative of the function. x2 + 3 y = x² – 3

A: Consider the given function y=x2+3x2-34

Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: Determine and distinguish the stationary values of the function f(x, y} = x² – 6x² – 8y². -

A: We need to find the stationary value of f(x,y)=x3-6x2-8y2   For that first we need to find the value…

Q: Use implicit differentiation in finding y' . x²y+xy² =6

A:

Q: Find the derivative of the given function. y = (4x2 + 4x)2 %3D O 32x° + 48x2+ 16x 64x + 96x2 + 32x O…

A: That's easy. Have a great day!!!

Q: Let f(x)= 3x^2+x-5. Using the definition of the derivative, find f’(x).

A:

Q: Use implicit differentiation to find y'. x2 - 4y2 = 12

A:

Q: Use the definition to compute the derivative of the function f (x) = Vx2 + 1.

A: We have to find derivative

Q: Determine whether the equation defines y as a function of x : xy + 2y = 1

A: we have to determine whether the given equation defines y as  a function of x. given:  xy+2y=1

Q: Find a function y(x) such that 5yy' = x and y(5) = 8. y =

A:

Q: Find the derivative of the function. g(x) = (2 + (x² + 7)*)3 ow) - 24(3)(2² + 7)*(2 + (x + 7)*)² ×…

A:

Q: Find the derivative of the function. f(x) 1 = - x6 + (x² + 4)(x² – x – 1) + 10

A:

Q: Find the derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)3

A:

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: does xy=4 describe y as a function of x?

A:

Q: Find yy as a function of xx if y′′′−8y′′−y′+8y=0 y(0)=4,  y′(0)=−6,  y′′(0)=130.

A:

Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x    . e…

A: Derivative of a function is the rate of change of function with respect to another variable.…

Q: Find the first and second derivatives of the function. f(x) = √3x-7     f '(x)=   f ''(x)=

A:

Q: Determine whether the equation defines y as a function of x. x =  |3y|

A: Given,           x =  |3y|

Q: Find the derivative of the function. 4 2x - x2 f(x) = %3D x2 - 6 f'(x) =

A: given,        fx=-x2-2x+4x2-6

Q: Determine whether y is a function of x…

A: For a function to be a function of x, the two variables say y and x must be separable…

Q: Find y as a function of x if y" +81y' = 0, y(0) = 4, y'(0) = -27, y"(0) = 81. %3D |

A: Given that y’’’ = 81y’ = 0 And y(0) = 4, y’(0) = -27, y’’(0) = 81 y(x) = ? y’’’ = 81y’ = 0 let d/dx…

Q: Find the derivative. y=(x+1)^2(x^2+1)^-3

A:

Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x.…

A: To find: Derivative of yy+1 with respect to x, assuming that y is implicitly a function of x.

Q: Find the derivative for each function. ㄷ 7. y=x² +2 9. y=2x²-x+3 A. 6. y=3x²-6 8. y=x²-3x+2 10.…

A:

Q: f (x) = 5x* f(x) %3D 12x5—4х4

A:

Q: Determine whether the equation y = ±√1 − 2x defines y as a function of x.

A:

Q: Find a function y(x) such that 2yy' and y(2) = 5. y(x) :

A: Given that 2yy'=x   and  y2=5. Solve the above equation as follows.…

Q: Find the derivative of the algebraic function. f(x) = (x3 − x)(x2 + 2)(x2 + x − 1)

A: Given information: fx=x3-xx2+2x2+x-1

Q: Find the derivative of the function. f(x)% 3D(x²+1)(x² + 10)/3 f'(x)%3D

A: Given equation

Q: Suppose that y is a function of x. Find y' if 2x°y - 3 = 2y + 5.

A:

Q: 3. у %3D 8 5. y = x6 1 7. у %3 x'

A:

Q: Find the function y(x) such that y′′(x) = 0 with y(1) = 2 and y′(1) =−1.

A: Given y′′(x) = 0 with y(1) = 2 and y′(1) =−1. y''(x)=0, with y(1)=2 and y'(1)=-1Now integrate both…

Q: Find a function y(x) such that 6yy' = x and y(6) = 3. y =

A: The objective of the question is solving the differential equation.

Q: 1) Determine whether the equation defines y as a function of x. x = y3

A: Givenx=y3

Q: Find y as a function of a if y(0) = 8, y(0) = 4, y"(0) = 134. y(x) = y"8y" -y + 8y = 0,

A:

Q: Write the first and second derivatives of the function f(x) = 4.2 In x7.1 |4) 4.2 f'(x) 4.2 f"(x) X

A: Consider the given function:

Q: Find the first and second derivatives of the function. w=((3+4z)/4z)(4-3z)

A:

Q: Find y as a function of x if x'y" – 9xy' + 25y = x", y(1) = 2, y'(1) = -5. y =

A:

Q: Consider the function f(x) = x3 + 4, and the point (1, 5). Write the equation of the line tangent to…

A: Compute the slope as follows.

Q: Find the derivative. F'(x) if F(x)= (ex¹ +5) 3 F'(x)=

A: