Compute the derivative for the following:
n(x) = sin(x^3-5x^2+4x-7)
Thanks,
andy
n' = cos(x^3-5x^2+4x-7) * (3x^2-10x+4)
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To compute the derivative of the function n(x) = sin(x^3 - 5x^2 + 4x - 7), you can use the chain rule along with the derivatives of basic trigonometric functions. Here's a step-by-step explanation of how to find the derivative:
1. Identify the function inside the sine function. In this case, it is x^3 - 5x^2 + 4x - 7.
2. Differentiate the function inside the sine function. Take the derivative of x^3 - 5x^2 + 4x - 7, which gives you 3x^2 - 10x + 4.
3. Now, apply the chain rule. The derivative of sin(u) with respect to x is cos(u) multiplied by the derivative of u with respect to x.
4. Plug in the result from step 2 into the chain rule. The derivative of sin(x^3 - 5x^2 + 4x - 7) with respect to x is cos(x^3 - 5x^2 + 4x - 7) multiplied by the derivative of (x^3 - 5x^2 + 4x - 7) with respect to x.
5. Simplify the expression obtained in step 4. The derivative of n(x) = sin(x^3 - 5x^2 + 4x - 7) is:
n'(x) = cos(x^3 - 5x^2 + 4x - 7) * (3x^2 - 10x + 4)
So, the derivative of the given function is n'(x) = cos(x^3 - 5x^2 + 4x - 7) * (3x^2 - 10x + 4).