CRL 4.10 MrG General Derivative Rules Exercises

3678 days ago by calcpage123

#1) f(x)=x^3 diff(f(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2}
#3) f(x)=x^(4/3)+5 diff(f(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{4}{3} \, x^{\left(\frac{1}{3}\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{4}{3} \, x^{\left(\frac{1}{3}\right)}
#5) f(x)=(x^2-3)^5 diff(f(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}10 \, {\left(x^{2} - 3\right)}^{4} x
\newcommand{\Bold}[1]{\mathbf{#1}}10 \, {\left(x^{2} - 3\right)}^{4} x
#7) f(x)=(3*x^2+2)*sqrt(1+5*x^2) (diff(f(x),x)).simplify_radical() 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{45 \, x^{3} + 16 \, x}{\sqrt{5 \, x^{2} + 1}}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{45 \, x^{3} + 16 \, x}{\sqrt{5 \, x^{2} + 1}}
#9) f(x)=5*x^4+3*x^2-6 diff(f(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}20 \, x^{3} + 6 \, x
\newcommand{\Bold}[1]{\mathbf{#1}}20 \, x^{3} + 6 \, x
#11) var('a,b') f(x)=x^(a+b) diff(f(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(a + b\right)} x^{{\left(a + b - 1\right)}}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(a + b\right)} x^{{\left(a + b - 1\right)}}
#13) f(x)=2/3*x^3-3/2*x^2+5 diff(f(x)) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, x^{2} - 3 \, x
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, x^{2} - 3 \, x
#15) var('c') f(x)=a+b*x+c*x^2 diff(f(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, c x + b
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, c x + b