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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$4 x ^ { 2 } + 5 \sqrt { 2 } x - 3$$

Differentiate w.r.t. x

$8x+5\sqrt{2}$

Steps Using Derivative Rule for Sum

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 $nax^{n-1}$.

$$2\times 4x^{2-1}+5\sqrt{2}x^{1-1}$$

Multiply $2$ times $4$.

$$8x^{2-1}+5\sqrt{2}x^{1-1}$$

Subtract $1$ from $2$.

$$8x^{1}+5\sqrt{2}x^{1-1}$$

Subtract $1$ from $1$.

$$8x^{1}+5\sqrt{2}x^{0}$$

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

$$8x+5\sqrt{2}x^{0}$$

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

$$8x+5\sqrt{2}\times 1$$

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

$$8x+5\sqrt{2}$$

Evaluate

$4x^{2}+5\sqrt{2}x-3$