Property 16
High Order Derivative
\(y=f(x)\)
\(\samefrac{dy}{dx}=\samefrac{df(x)}{dx}=f'(x)\qquad\text{first derivative}\)
\(\samefrac{d^2y}{dx^2}=\samefrac{d^2f(x)}{dx^2}=f''(x)\qquad\text{second derivative}\)
\(\samefrac{d^ny}{dx^n}=\samefrac{d^nf(x)}{dx^n}=f^{(n)}(x)\qquad n^{\text{th}}\text{ derivative}\)
1.
\(f(x)=x^7\)
\(\Rightarrow\samefrac{d^{7}f(x)}{dx^{7}}=?\)
2.
\(f(x)=e^x\)
\(\Rightarrow\samefrac{d^{30}f(x)}{dx^{30}}=?\)
3.
\(f(x)=e^{2x}\)
\(\Rightarrow\samefrac{d^{10}f(x)}{dx^{10}}=?\)
4.
\(f(x)=\samefrac1x\)
\(\Rightarrow\samefrac{d^{20}f(x)}{dx^{20}}=?\)
5.
\(f(x)=\ln x\)
\(\Rightarrow\samefrac{d^{14}f(x)}{dx^{14}}=?\)
6.
\(f(x)=\ln(x)^{10}\)
\(\Rightarrow\samefrac{d^{10}f(x)}{dx^{10}}=?\)
7.
\(f(x)=\ln(x+3)\)
\(\Rightarrow\samefrac{d^{8}f(x)}{dx^{8}}=?\)