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 $nax^{n-1}$.

$$3y^{3-1}+2\left(-28\right)y^{2-1}+142y^{1-1}$$

Subtract $1$ from $3$.

$$3y^{2}+2\left(-28\right)y^{2-1}+142y^{1-1}$$

Multiply $2$ times $-28$.

$$3y^{2}-56y^{2-1}+142y^{1-1}$$

Subtract $1$ from $2$.

$$3y^{2}-56y^{1}+142y^{1-1}$$

Subtract $1$ from $1$.

$$3y^{2}-56y^{1}+142y^{0}$$

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

$$3y^{2}-56y+142y^{0}$$

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

$$3y^{2}-56y+142\times 1$$

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

$$3y^{2}-56y+142$$

Show Solution

Evaluate

$y^{3}-28y^{2}+142y-120$

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Example

Question

Differentiate w.r.t. y

Steps Using Derivative Rule for Sum

Evaluate