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Try this.
If y=cosx find dy/d5x
please show workings
#thanks
To find dy/d5x, we need to use the chain rule in calculus. The chain rule states that if we have a function y=f(g(x)), then the derivative(dy/dx) is given by dy/dx = (dy/dg) * (dg/dx).
In this case, y = cos(x), which means f(x) = cos(x). Let's define another function g(x) = 5x.
Now, we need to find dy/d5x. To do this, we'll follow these steps:
Step 1: Find the derivative of y = cos(x) with respect to x, which is dy/dx.
dy/dx = -sin(x) (derivative of cos(x) is -sin(x))
Step 2: Find the derivative of g(x) = 5x with respect to x, which is dg/dx.
dg/dx = 5 (derivative of 5x is 5)
Step 3: Substitute the derivatives from steps 1 and 2 into the chain rule equation.
dy/d5x = (dy/dx) * (dx/d5x)
Step 4: Substitute dy/dx and dx/d5x into the equation from step 3.
dy/d5x = (-sin(x)) * (1/5) [because dx/d5x = (1/5)]
Therefore, dy/d5x = (-sin(x)) * (1/5).