Power
What is the derivative of
f(x)=2x^47
f'(x)=94x^46
What is the derivative of:
f(x)=1/x
f'(x)=-x^-2=-1/x^2
What is the derivative of:
f(x)=2cosx
f'(x)=-2sinx
What is the derivative of:
f(x)=-5e^x
f'(x)=-5e^x
What is the derivative of:
f(x)=1+5lnx
f'(x)=5/x
What is the derivative of:
f(x)=5\sqrtx
f'(x)=5/2 x^{-1/2}=5/(2\sqrtx)
What is the derivative of:
f(x)=(x+1)/x
f'(x)=-x^-2=-1/x^2
What is the derivative of:
f(x)=sin(x^2)
f'(x)=(2x)(cos x^2)
What is the derivative of:
f(x)=e^(3x^2-1)
f'(x)=(6x)(e^(3x^2-1))
What is the derivative of:
f(x)=ln (9x)
f'(x)=(1/(9x))(9)=1/x
What is the derivative of:
f(x)=3/x^8
f'(x)=-24x^-9=-24/x^9
What is the derivative of:
f(x)=x/(x+1)
f'(x)=((x+1)(1)-(x)(1))/(x+1)^2=1/(x+1)^2
What is the derivative of:
f(x)=tanx+cotx
f'(x)=sec^2x-csc^2x
What is the derivative of:
f(x)=2^x
f'(x)=(2^x)(ln 2)
What is the derivative of:
f(x)=ln(x^7)
f'(x)=(1/x^7)(7x^6)=7/x
What is the derivative of:
f(x)=7/\root{3}{x}
f'(x)=-7/3x^{-4/3}=-7/(3\root{3}{x^4})
What is the derivative of:
f(x)=x/e^x
f'(x)=((e^x)(1)-(x)(e^x))/(e^(2x))=(1-x)/e^x
What is the derivative of:
secx + cscx
f'(x)=(secx)(tanx)-(cscx)(cotx)
What is the derivative of:
f(x)=5^(x^2)
f'(x)=(5^(x^2))(ln5)(2x)
What is the derivative of:
f(x)=ln (C/x)
f'(x)=(x/C)(-C/x^2)=-1/x
What is the SECOND derivative of:
f(x)=x^-1
f''(x)=2x^-3=2/x^3
What is the SECOND derivative of:
f(x)=x/e^x
f''(x)=((e^x)(-1)-(1-x)(e^x))/(e^(2x))=(x-2)/e^x
What is the SECOND derivative of:
f(x)=(x)(sinx)
f''(x)=2cosx-(x)(sinx)
What is the SECOND derivative of:
f(x)=e^(ln x^4)
f''(x)=12x^2
What is the SECOND derivative of:
f(x)=(x)(ln x)
f''(x)=1/x