d/dx(3sin(-5x)=
To differentiate the function y = 3sin(-5x), we can use the chain rule. The chain rule states that if we have a composite function y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).
In this case, f(u) = 3sin(u) and g(x) = -5x. Taking the derivative of f(u) with respect to u gives f'(u) = 3cos(u). Taking the derivative of g(x) with respect to x gives g'(x) = -5.
Applying the chain rule, we have dy/dx = f'(g(x)) * g'(x) = 3cos(-5x) * (-5) = -15cos(-5x).
Therefore, d/dx(3sin(-5x)) = -15cos(-5x).
To differentiate the given function, 3sin(-5x), with respect to x, we can use the chain rule and the derivative of the sine function.
The chain rule states that if we have a composition of functions, f(g(x)), then the derivative can be found by multiplying the derivative of the outer function, f'(g(x)), with the derivative of the inner function, g'(x).
In this case, we have the function f(x) = 3sin(x), where the inner function g(x) = -5x.
First, let's find the derivative of the outer function, which is just the derivative of sine function:
d/dx(sin(x)) = cos(x)
Now, let's find the derivative of the inner function by applying the power rule:
d/dx(-5x) = -5
Next, we can apply the chain rule and multiply the derivatives:
d/dx(3sin(-5x)) = 3 * cos(-5x) * (-5)
The cosine function is an even function, which means cos(-x) = cos(x). Therefore, we simplify further:
d/dx(3sin(-5x)) = -15cos(5x)
So, the derivative of the function 3sin(-5x) with respect to x is -15cos(5x).
To find the derivative of the function f(x) = 3sin(-5x), we can use the chain rule. The chain rule states that if we have a composition of functions, such as f(g(x)), the derivative can be found by taking the derivative of the outer function with respect to the inner function and then multiplying it by the derivative of the inner function with respect to x.
In this case, the outer function is 3sin(u), where u = -5x, and the inner function is u = -5x.
Step 1: Find the derivative of the outer function with respect to the inner function.
The derivative of sin(u) with respect to u is cos(u).
Step 2: Find the derivative of the inner function with respect to x.
The derivative of -5x with respect to x is -5.
Step 3: Multiply the derivatives found in steps 1 and 2.
cos(u) * -5
Step 4: Substitute the value of u back into the expression.
cos(-5x) * -5
Therefore, the derivative of 3sin(-5x) with respect to x is -5cos(-5x), which can also be written as -5cos(5x).