What is the derivative of 3sin(4x)? I have no idea where to begin!!!
3 d/dx sin (4x)
note: d/dx sin u = cos u * du/dx
3 cos (4x) * d/dx (4x)
3 cos (4x) * 4
12 cos(4x)
What is the answer to the equation
To find the derivative of the function 3sin(4x), you can use the chain rule. The chain rule states that if you have a composite function, the derivative is found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.
Let's break it down step by step:
1. Start by differentiating the outer function: sin(4x). The derivative of sin(x) is cos(x), so the derivative of sin(4x) would be cos(4x).
2. Next, take the derivative of the inner function, which is 4x. The derivative of 4x is simply 4.
3. Now, using the chain rule, multiply the derivative of the outer function (cos(4x)) by the derivative of the inner function (4).
cos(4x) * 4 = 4cos(4x)
So, the derivative of 3sin(4x) is 4cos(4x).
Remember that this is just one way to find the derivative using the chain rule. You can also use other methods such as implicit differentiation or the product rule depending on the complexity of the function.
To find the derivative of 3sin(4x), you can use the chain rule. The chain rule states that if you have a function of the form g(f(x)), the derivative of g(f(x)) with respect to x is given by g'(f(x)) * f'(x).
In this case, g(u) = 3u and f(x) = sin(4x). The derivative of g(u) with respect to u is 3, and the derivative of f(x) with respect to x is cos(4x) * 4.
Now we can apply the chain rule. Multiply the derivative of g(u) by the derivative of f(x) to get:
3 * cos(4x) * 4
Simplifying this expression gives:
12 * cos(4x)
Therefore, the derivative of 3sin(4x) is 12cos(4x).