Find the derivative of fog(x) is f(x)= 2x-3 and g(x) = x^2-2
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Rylan Hills
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We have f(x)= 2x-3 and g(x) = x^2 - 2
fog(x) = f(g(x))
=> f( x^2 - 2)
=> 2*(x^2 - 2) - 3
=> 2x^2 - 4 - 3
=> 2x^2 - 7
The derivative of 2x^2 - 7 = 4x
The required derivative is 4x.
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hala718
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Given f(x)= 2x-3
g(x) = x^2 -2
We need to find fog'(x)
First we need to determine the function fog(x).
==> fog(x)= f(g(x) = 2g(x) -3
= 2(x^2-3) -3
==> fog(x) = 2x^2 -6 -3 = 2x^2 -9
==> fog(x)= 2x^2 -9
Now we will differentiate.
==> fog'(x)= 4x
Then the derivative of fog(x) is fog'(x)= 4x