Answer:
20
Step-by-step explanation:
Given function f(x)=
We need to find f(-4) which means we need to find the value of the function when x=-4 .
On substituting x=-4 in the given function:
f(-4)=
Square of -4 is 16.
Hence, f(-4)=
=
Hence the value of the given function f(x)= when x=-4 is 20.
Answer:
Step-by-step explanation:
So we have:
And we want to find dy/dx.
So, let's take the derivative of both sides with respect to x:
Let's do each side individually.
Left Side:
We have:
We can use the product rule:
So, our derivative is:
We must implicitly differentiate for y. This gives us:
For the sin(y), we need to use the chain rule:
Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.
So, our derivative is:
Simplify:
And we are done for the right.
Right Side:
We have:
This will be significantly easier since it's just x like normal.
Again, let's use the product rule:
Differentiate:
So, our entire equation is:
To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:
Finally, divide everything by the expression inside the parentheses to obtain our derivative:
And we're done!
