Derivative of tan(x)^7
Answer
7*sec(x)^2*tan(x)^6
Derivative of tan(x)^7
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in : use the chain rule = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
- Differentiate the outer function, then multiply by the inner derivative.
- Final answer: ec(x)^an(x)^6
The derivative of tan(x)^7 is 7*sec(x)^2*tan(x)^6.
Instant step-by-step solution for tan(x)^7
Share this result
Derivative of tan(x)^7 = 7*sec(x)^2*tan(x)^6 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-tanx-minus-to-minus-the-minus-7
How to find the derivative of tan(x)^7
To find the derivative of tan(x)^7, we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of -x
Solve d/dx -x
Derivative of x^(1/2)
Solve d/dx x^(1/2)
Derivative of sqrt(x)
Solve d/dx sqrt(x)
Derivative of x^3
Solve d/dx x^3
Derivative of x*e^x
Solve d/dx x*e^x
Derivative of x*ln(x)
Solve d/dx x*ln(x)
Derivative of x+1
Solve d/dx x+1
Derivative of x^2
Solve d/dx x^2
Derivative of x^2-1
Solve d/dx x^2-1
Derivative of x^2+1
Solve d/dx x^2+1
Frequently Asked Questions
What is the derivative of tan(x)^7?▼
The derivative of tan(x)^7 is 7*sec(x)^2*tan(x)^6.
How do you find the derivative of tan(x)^7?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 7*sec(x)^2*tan(x)^6.
Why is the derivative of tan(x)^7 equal to 7*sec(x)^2*tan(x)^6?▼
Because differentiation measures how a function changes — applying the rules to tan(x)^7 yields 7*sec(x)^2*tan(x)^6. See the full step-by-step breakdown above.