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Higher Order Derivatives

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Wize University Calculus 1 Textbook > Derivatives

Higher Order Derivatives

4 Activities

An object is thrown straight up in the air at t=0t = 0 seconds. Its height in metres at tt seconds is given by

h(t)=s0+v0t−7t2h(t) = s_0 + v_0 t - 7t^2
where s0s_0 and v0v_0 are constants. In the first second the object rises 7 metres. For how many seconds does the object rise before starting to fall back down?
More Higher Order Derivatives Questions:
Higher Order Derivatives: The Power Rule
If f(x)=x10f\left(x\right)=x^{10} find f(9)(x)f^{\left(9\right)}\left(x\right).
(i.e. the 9th derivative)
Higher Order Derivatives
Find the second derivative of f(x)=x2+16xf(x) = x^2+16\sqrt{x}.
Higher order derivatives
Consider the function f(x)=3x−4xf(x)=\dfrac{3x-4}{x}. Find the second derivative f′′(x), at x=1f''(x),\text{ at }x=1.
Higher order derivatives
Consider the function f(x)=3x−4xf(x)=\dfrac{3x-4}{x}. Find the second derivative f′′(x), at x=1f''(x),\text{ at }x=1.
The Chain Rule
If 2−g(x)=x2+2[f(x)]2−x3g(x)2-g\left(x\right)=x^2+2\left[f\left(x\right)\right]^2-x^3g\left(x\right), f(0)=1 , f′(0)=−2, g(0)=−1 and  g′′(0)=3f\left(0\right)=1\ ,\ f'\left(0\right)=-2,\ g\left(0\right)=-1\ \text{and}\ \ g''\left(0\right)=3, then the value of f′′(0)f''\left(0\right) is equal to
Higher Order Derivatives
If f(x)=sin⁡(2x)f\left(x\right)=\sin\left(2x\right), find f(21)(π2)f^{\left(21\right)}\left(\frac{\pi}{2}\right).
(i.e. find the 21st derivative at the point π2\frac{\pi}{2})
Higher Order Derivatives
If f(x)=sin⁡(2x)f\left(x\right)=\sin\left(2x\right), find f(21)(π2)f^{\left(21\right)}\left(\frac{\pi}{2}\right).
(i.e. find the 21st derivative at the point π2\frac{\pi}{2})
Higher order derivatives
Consider the function f(x)=3x−4xf(x)=\dfrac{3x-4}{x}. Find the second derivative f′′(x), at x=1f''(x),\text{ at }x=1.
The Chain Rule
If 2−g(x)=x2+2[f(x)]2−x3g(x)2-g\left(x\right)=x^2+2\left[f\left(x\right)\right]^2-x^3g\left(x\right), f(0)=1 , f′(0)=−2, g(0)=−1 and  g′′(0)=3f\left(0\right)=1\ ,\ f'\left(0\right)=-2,\ g\left(0\right)=-1\ \text{and}\ \ g''\left(0\right)=3, then the value of f′′(0)f''\left(0\right) is equal to
Higher Order Derivatives: The Power Rule
If f(x)=x10f\left(x\right)=x^{10} find f(9)(x)f^{\left(9\right)}\left(x\right).
(i.e. the 9th derivative)
Higher Order Derivatives
Find the third derivative of f(x)=x2+16xf(x) = x^2+16\sqrt{x}.
Higher Order Derivatives
If f(x)=sin⁡(2x)f\left(x\right)=\sin\left(2x\right), find f(21)(π2)f^{\left(21\right)}\left(\frac{\pi}{2}\right).
(i.e. find the 21st derivative at the point π2\frac{\pi}{2})
Higher order derivatives
Consider the function f(x)=3x−4xf(x)=\dfrac{3x-4}{x}. Find the second derivative f′′(x), at x=1f''(x),\text{ at }x=1.