Find the derivative of g(t)=4t+t^(-4)-2*sqrt(2), At an arbitrary point, I have used 1 so far I am at 4x1, 4+1/1^4-2*sqrt(2), don't know how to proceed and Wolfram wasn't helpful.

Cheers.

Question

Find the derivative of g(t)=4t+t^(-4)-2*sqrt(2), At an arbitrary point, I have used 1 so far I am at 4x1, 4+1/1^4-2*sqrt(2), don't know how to proceed and Wolfram wasn't helpful. 

Cheers.

anonymous · Answer

$$g(t)=4t+t^{-4}-2 \times \sqrt(2) $$
$$= 4 - 4t^{-3}$$

anonymous · Answer

sorry its -4t^-5

anonymous · Answer

=4-4t^-5 that is? How'd it come to that, does a negative exponent increase rather than decrease when using the power rule?

anonymous · Answer

ya the rule says
$$x^n = nx^{n-1}$$
$$\frac{ d }{ dx } t^{-4} = -4t^{-4-1} = -4t^{-5}$$

anonymous · Answer

Ahh thanks, I sometimes get my negatives confused as what is less/more. Since 2*sqrt(2) is a constant it's deriv is 0 thus 4t-t^-5 deriv - 0 thus staying the same?