Power & Constant Rules
Find the derivative of f(x) = x⁷
f′(x) = 7x⁶
Use the Product Rule to differentiate f(x) = x² · sin(x)
f′(x) = 2x·sin(x) + x²·cos(x)
Differentiate f(x) = (3x + 5)⁴
f′(x) = 12(3x + 5)³
What is the derivative of sin(x)?
cos(x)
What is the derivative of eˣ?
eˣ
Find the derivative of f(x) = 12
f′(x) = 0
Use the Quotient Rule to differentiate f(x) = x² / (x + 1)
f′(x) = (x² + 2x) / (x+1)²
Differentiate f(x) = sin(x²)
f′(x) = 2x·cos(x²)
What is the derivative of tan(x)?
sec²(x)
What is the derivative of ln(x)?
1/x
Find the derivative of f(x) = 4x³ − 5x + 2
f′(x) = 12x² − 5
Use the Product Rule to differentiate f(x) = eˣ · x³
f′(x) = eˣ(x³ + 3x²)
Differentiate f(x) = √(5x − 1)
f′(x) = 5 / (2√(5x−1))
Differentiate f(x) = 5cos(x) − 3sin(x)
f′(x) = −5sin(x) − 3cos(x)
Differentiate f(x) = e^(3x)
f′(x) = 3e^(3x)
Find the derivative of f(x) = x^(1/2)
f′(x) = (1/2)x^(−1/2) or 1/(2√x)
Use the Quotient Rule to differentiate f(x) = sin(x) / x
f′(x) = (x·cos(x) − sin(x)) / x²
Differentiate f(x) = (x² + 3x)⁵
f′(x) = 5(x² + 3x)⁴ · (2x + 3)
What is the derivative of sec(x)?
sec(x)tan(x)
Differentiate f(x) = ln(x² + 1)
f′(x) = 2x / (x² + 1)
Find the derivative of f(x) = 3x⁵ − 7x³ + x − 9
f′(x) = 15x⁴ − 21x² + 1
Differentiate f(x) = (x² + 1)(x³ − 2x) using the Product Rule
f′(x) = 5x⁴ − 4x² − 2
Differentiate f(x) = cos³(x)
f′(x) = −3cos²(x)sin(x)
Differentiate f(x) = sin(x)·cos(x)
f′(x) = cos²(x) − sin²(x), also written as cos(2x)
Differentiate f(x) = 5eˣ + ln(x) − x²
f′(x) = 5eˣ + 1/x − 2x