f'(x)=
the equation is below

Question

f'(x)= 
the equation is below

anonymous · Answer

$$f(x)=6\sqrt{x}(x^3-8\sqrt{x}+7)$$

anonymous · Answer

2) f(t)=(In8)^t

zehanz · Answer

First one: write everthing as powers of x, then expand the brackets and differentiate term-by-term.
So:$$f(x)=6x^{\frac{1}{2}}(x^3-8x^{\frac{1}{2}}+7)=6x^{3\frac{ 1 }{ 2 }} - .........$$

zehanz · Answer

Second one is of the form:$$f(t)=a^t$$so$$f'(t)=\ln a \cdot a^t$$In this function a = ln8.

anonymous · Answer

For the first answer, is it 20x(7/3)-48x+21x^(-1/2)

anonymous · Answer

the second one is In64^t?

zehanz · Answer

First one: $$f(x)=6x^{3.5}-48x+42x^{0.5}$$So $$f'(x)=21x^{2.5}-48+21x^{-0.5}$$Now write with radicals again:$$f'(x)=21x^2\sqrt{x}-48+\frac{ 21 }{ \sqrt{x} }$$

zehanz · Answer

Second one:$$f(t)=(\ln8)^t$$So$$f'(t)=\ln(\ln 8)\cdot (\ln 8)^t$$because a = ln 8 (see my first remark about the derivative of an exponential function).