how do I go about this the high power exponents has me lost
t(x)=x^5 - 2x^3 + 4x^2 + 5
whats the gradient of tangent line when x=2
Just use the formula $\displaystyle \frac{d}{dx}x^n=nx^{n-1}$
This is true for all exponents $\displaystyle n$.
The derivative of $\displaystyle x^5$ is $\displaystyle 5x^4$. If there is a constant, such as in the function $\displaystyle 2x^3$, you just mulitply it by the exponent. So the derivative is just $\displaystyle 6x^2$.
So what is the derivative of $\displaystyle x^5- 2x^3 + 4x^2 + 5$ ???