How to solve 5p ^ 2 - 2sp + 20

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.

$$2\times 5p^{2-1}+\left(-2s\right)p^{1-1}$$

Multiply $2$ times $5$.

$$10p^{2-1}+\left(-2s\right)p^{1-1}$$

Subtract $1$ from $2$.

$$10p^{1}+\left(-2s\right)p^{1-1}$$

Subtract $1$ from $1$.

$$10p^{1}+\left(-2s\right)p^{0}$$

For any term $t$, $t^{1}=t$.

$$10p+\left(-2s\right)p^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$10p+\left(-2s\right)\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$10p-2s$$

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Evaluate

$5p^{2}-2ps+20$

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Example

Question

Differentiate w.r.t. p

Steps Using Derivative Rule for Sum

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