Product Rule
f(x) = 2x^2 cosx
What is f'(x) = 2x^2(-sinx) + cosx(4x)
The product rule tells us that the derivative of the product of two functions is equal to:
1st function(deriv. of 2nd) + (2nd func.)(deriv. of 1st)
y = x^-1
y' = -x^-2
To find the derivative of a power function, you multiply the coefficient by the power and subtract the exponent by 1.
f(x) = x^2 - 4/2x-2
f'(x) = (2x-2)(2x) - (x^2 - 4)(2)/(2x-2)^2
The quotient rule tells us the the derivative of u/v equals v u' - u v'/v^2
f(x) = 2cosx - 3x^2
f'(x) = 2-sinx - 6x
The sum & difference rule tells us that the derivative of a sum or difference is the derivatives + or - each other
f(x) = 4csc
f'(x) = -4 csc cotx
f(x) = (3x-2)sinx
What is f'(x) = (3x-2)(cosx) + sinx(3)?
The product rule tells us that the derivative of the product of two functions is equal to: 1st function(deriv. of 2nd) + (2nd func.)(deriv. of 1st)
y = 1/x^3
y' = -3x^-4
To find the derivative of a power function, you multiply the coefficient by the power and subtract the exponent by 1.
f(x) = 3x/4x^2
f'(x) = 4x^2(3) - 3x(8x) /(4x^2)^2
The quotient rule tells us the the derivative of u/v equals v u' - u v'/v^2
f(x) = sinx + 6lnx
f'(x) = cosx + 6/x
The sum & difference rule tells us that the derivative of a sum or difference is the derivatives + or - each other
f(x) = 4tanx + 2cos x
f'(x) = 4 sec^2 x - 2sinx
The constant multiple rule tells us that when finding the derivative, we keep the same coefficient and multiply it by the derivative
f(x) = (2x^2 - 3x)cos x
What is f'(x) = (2x^2 -3x)(-sinx) + cosx(4x-3)
The product rule tells us that the derivative of the product of two functions is equal to:
1st function(deriv. of 2nd) + (2nd func.)(deriv. of 1st)
y = x^7/3
y' = 7/3x^4/3
To find the derivative of a power function, you multiply the coefficient by the power and subtract the exponent by 1.
f(x) = 2x^5 +4/x^3
f'(x) = x^3(10x^4) - (2x^5 +4)(3x^2)/(x^3)^2
The quotient rule tells us the the derivative of u/v equals v u' - u v'/v^2
f(x) = tanx + x^3
f'(x) = sec^2x - 3x^2
The sum & difference rule tells us that the derivative of a sum or difference is the derivatives + or - each other
f(x) = tanx
f'(x) = sec^2x
The constant multiple rule tells us that when finding the derivative, we keep the same coefficient and multiply it by the derivative
f(x) = 5x^2(3x^4)
f'(x) = 5x^2(12x^3) + 3x^4(10x)
The product rule tells us that the derivative of the product of two functions is equal to:
1st function(deriv. of 2nd) + (2nd func.)(deriv. of 1st)
y = x^3/4
y' = 3/4x^-1/4
To find the derivative of a power function, you multiply the coefficient by the power and subtract the exponent by 1.
f(x) = 3x^3 - 5/x^2
f'(x) = x^2(9x^2) - (3x^3 - 5)(2x)/(x^2)^2
The quotient rule tells us the the derivative of u/v equals v u' - u v'/v^2
f(x) = cscx - 4x^5
f'(x) = -csc cotx - 20x^4
The sum & difference rule tells us that the derivative of a sum or difference is the derivatives + or - each other
f(x) = 42 cos x - 6cotx
f'(x) = -42 sinx + 6csc^2x
The constant multiple rule tells us that when finding the derivative, we keep the same coefficient and multiply it by the derivative