Function Derivative Calculator

Solving 2nd order derivatives of a function

1) Solve the derivative for the function  f(x) =  x^2 + 8x + 9

Solution :  The given function is  f(x) = x^2 + 8x + 9

Differentiate the above equation with respect to 'x' . It is represented as f'(x) .

f'(x)  =   `(d(x^2))/dx`   +  `(d(8x))/dx`   +  `(d(9))/dx` .

f'(x)   =     2x   +   8   +   0

f'(x)    =     2x    +   8   .

The answer is   f'(x)  =  2x  +  8 .

2) Solve the derivative for the function   f(y)  =  y^2  +  10y  + 3

Solution :   The given function is  f(y)  =  y^2  +  10y  +  3

Differentiate the above equation with respect to 'y' . It is represented as f'(y)  .

f'(y)  = `(d(y^2))/dy`   +  `(d(10y))/dy`   +   `(d(3))/dy`

f'(y)  =   2y   +  10   +   0

f'(y)  =   2y   +   10

The answer is  f'(y) = 2y  +  10

Solving third Order Derivative Functions

1) Find the derivative of the function  f(x)  =  x3 + 3x^2 + 18x  +  20

Solution : The given   function  f(x)  =  x3 + 3x^2 + 18x  +  20

Differentiate the above function with respect to 'x' .

f'(x)  =  3 x^2   +  3  ( 2 ) x   +  18   +  0

f'(x)   =  3x^2  +  6x  +  18  .

The answer is   f'(x)   =  3x^2  +  6x  +  18  .

2) Find the derivative for   f(x)  =  6x3  + 5x^2  +  3x  +  1

Solution : The given function is f(x)  =  6x3  + 5x^2  +  3x  +  1

Differentiate the above f(x) with respect to 'x'  .

f'(x)  =  6 (3)x^2  +  5 (2)x   +  3  + 0

f'(x)   =  18x^2   +  10x   +  3

The answer is  f'(x)   =  18x^2   +  10x   +  3

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Solving 4th Order Derivative Function

1) Solve the derivative for the function  f(y) = y^4  + 3y^3  +  5y^2  + 4y  +  9

Solution : The given function  f(y) = y^4  + 3y^3  +  5y^2  + 4y  +  9

DIfferentiate the above equation with respect to 'y' .

f'(y)  =  4y^3  +  3(3)y^2  +  5(2)y  +  4  +  0

f'(y)  =  4y^3   +  9y^2  + 10y   +  4

The answer is    f(y) = y^4  + 3y^3  +  5y^2  + 4y  +  9

2) Solve the derivative for the function f(y)  =  6y^4  +  y^3   +  y^2  + 10 y  + 3

Solution :  The given function  is    f(y)  =  6y^4  +  y^3   +  y^2  + 10 y  + 3

DIfferentiate the above equation with respect to 'y' .

f'(y)   =  6(4)y^3   +  3y^2    +  2y   +  10  +   0

f'(y)   =   24y^3   +  3y^2   +  2y   +  10

The answer is    f'(y)   =   24y^3   +  3y^2   +  2y   +  10

Algebra is widely used in day to day activities watch out for my forthcoming posts on Derivative Calculator and Derivative of Natural log. I am sure they will be helpful.