To derive sech(sinx)^2, we will use the chain rule and the definition of sech(x). The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. The definition of sech(x) is 1/cosh(x).

Step 1: Write down the function
f(x) = sech(sinx)^2

Step 2: Apply the chain rule
f'(x) = 2 * sech(sinx) * -sech(sinx) * tanh(sinx) * cos(x)

Step 3: Simplify the expression
f'(x) = -2 * sech^2(sinx) * tanh(sinx) * cos(x)

So, the derivative of sech(sinx)^2 is -2 * sech^2(sinx) * tanh(sinx) * cos(x).

Question

To derive sech(sinx)^2, we will use the chain rule and the definition of sech(x). The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. The definition of sech(x) is 1/cosh(x).

Step 1: Write down the function
f(x) = sech(sinx)^2

Step 2: Apply the chain rule
f'(x) = 2 * sech(sinx) * -sech(sinx) * tanh(sinx) * cos(x)

Step 3: Simplify the expression
f'(x) = -2 * sech^2(sinx) * tanh(sinx) * cos(x)

So, the derivative of sech(sinx)^2 is -2 * sech^2(sinx) * tanh(sinx) * cos(x).

Knowee AI · Accepted Answer

To derive sech(sinx)^2, we will use the chain rule and the definition of sech(x). The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. The definition of sech(x) is 1/cosh(x).

Step 1: Write down the function
f(x) = sech(sinx)^2

Step 2: Apply the chain rule
f'(x) = 2 * sech(sinx) * -sech(sinx) * tanh(sinx) * cos(x)

Step 3: Simplify the expression
f'(x) = -2 * sech^2(sinx) * tanh(sinx) * cos(x)

So, the derivative of sech(sinx)^2 is -2 * sech^2(sinx) * tanh(sinx) * cos(x).

derive sech(sinx)^2

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