Derivative of sin(x^7)
Answer
7*cos(x^7)*x^6
Derivative of sin(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: os()*
The derivative of sin(x^7) is 7*cos(x^7)*x^6.
Instant step-by-step solution for sin(x^7)
Share this result
Derivative of sin(x^7) = 7*cos(x^7)*x^6 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sinx-minus-to-minus-the-minus-7
How to find the derivative of sin(x^7)
To find the derivative of sin(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^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
Derivative of x^4
Solve d/dx x^4
Derivative of cos(2x)
Solve d/dx cos(2x)
Derivative of cos(x)^2
Solve d/dx cos(x)^2
Derivative of cos(x)
Solve d/dx cos(x)
Derivative of cosh(x)
Solve d/dx cosh(x)
Derivative of cot(x)
Solve d/dx cot(x)
Derivative of csc(x)
Solve d/dx csc(x)
Frequently Asked Questions
What is the derivative of sin(x^7)?▼
The derivative of sin(x^7) is 7*cos(x^7)*x^6.
How do you find the derivative of sin(x^7)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 7*cos(x^7)*x^6.
Why is the derivative of sin(x^7) equal to 7*cos(x^7)*x^6?▼
Because differentiation measures how a function changes — applying the rules to sin(x^7) yields 7*cos(x^7)*x^6. See the full step-by-step breakdown above.