Problems
-
Determine the derivative of $f(g(x))$ where $f(x)=\sin(x)$ and $g(x)=x^2+4$.
-
Find the derivative of $[f(x)]^n$ where $f(x)$ is differentiable and $n$ is an integer.
-
Determine the derivative of $(x^2-1)^{100}$.
-
Determine $(f\circ g)'(x)$ if $f(x)=(x-1)/(x+1)$ and $g(x)=x^2$.
-
Determine $(f\circ g)'(x)$ if $f(x)=2x$ and $g(x)=3x$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=2\,x-2\,x^2$ and $g(x)=1-2\,x$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=-x-1$ and $g(x)=-3\,x^2$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=2\,x^2+4\,x-1$ and $g(x)=3\,x^2+2\,x-3$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=-x^2-5$ and $g(x)=x+5$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=2\,x^2+4\,x-4$ and $g(x)=-5\,x^2+2\,x+6$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=x^2-6\,x-4$ and $g(x)=-3\,x^2-2\,x-7$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=-2\,x^2-4$ and $g(x)=-x$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=-x^2-8\,x-6$ and $g(x)=9\,x^2+4\,x+3$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=5$ and $g(x)=x^2+8\,x+3$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=2\,x^2-1$ and $g(x)=2\,x^2+2$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=2\,x^2+x-1$ and $g(x)=0$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=2\,x^2+2\,x-2$ and $g(x)=-2\,x^2+x-1$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=-2\,x^2+x+2$ and $g(x)=2\,x^2+2\,x-2$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=2\,x-x^2$ and $g(x)=x^2-x+2$.
-
Determine the derivative of $(f\circ g)(x)$ where $f(x)=2$ and $g(x)=-2\,x-2$.
