Derivative of sin(x^2+6)
Answer
2*cos(6+x^2)*x
Derivative of sin(x^2+6)
- 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(6+)*x
The derivative of sin(x^2+6) is 2*cos(6+x^2)*x.
Instant step-by-step solution for sin(x^2+6)
Share this result
Derivative of sin(x^2+6) = 2*cos(6+x^2)*x Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sinx-minus-to-minus-the-minus-2-minus-plus-minus-6
How to find the derivative of sin(x^2+6)
To find the derivative of sin(x^2+6), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of 5x
Solve d/dx 5x
Derivative of Abs(x)
Solve d/dx Abs(x)
Derivative of acos(x)
Solve d/dx acos(x)
Derivative of asin(x)
Solve d/dx asin(x)
Derivative of atan(x)
Solve d/dx atan(x)
Derivative of x^(1/3)
Solve d/dx x^(1/3)
Derivative of e^(2x)
Solve d/dx e^(2x)
Derivative of e^(-x)
Solve d/dx e^(-x)
Derivative of e^x
Solve d/dx e^x
Derivative of ln(2x)
Solve d/dx ln(2x)
Frequently Asked Questions
What is the derivative of sin(x^2+6)?▼
The derivative of sin(x^2+6) is 2*cos(6+x^2)*x.
How do you find the derivative of sin(x^2+6)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 2*cos(6+x^2)*x.
Why is the derivative of sin(x^2+6) equal to 2*cos(6+x^2)*x?▼
Because differentiation measures how a function changes — applying the rules to sin(x^2+6) yields 2*cos(6+x^2)*x. See the full step-by-step breakdown above.