# Math Help - differentiation

1. ## differentiation

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

2. Originally Posted by wolfhound
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 $\frac{d}{dx}x^n=nx^{n-1}$

This is true for all exponents $n$.

The derivative of $x^5$ is $5x^4$. If there is a constant, such as in the function $2x^3$, you just mulitply it by the exponent. So the derivative is just $6x^2$.

So what is the derivative of $x^5- 2x^3 + 4x^2 + 5$ ???

3. Originally Posted by adkinsjr
Just use the formula $\frac{d}{dx}x^n=nx^{n-1}$

This is true for all exponents $n$.

The derivative of $x^5$ is $5x^4$. If there is a constant, such as in the function $2x^3$, you just mulitply it by the exponent. So the derivative is just $6x^2$.

So what is the derivative of $x^5- 2x^3 + 4x^2 + 5$ ???
5x^4- 6x^2 + 8x
so gradient is 72?