Solve 9(x)^(2)+6x+12-10(x)^(2)+12-6x | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$9 { x }^{ 2 } +6x+12-10 { x }^{ 2 } +12-6x$$

Evaluate

$24-x^{2}$

Solution Steps

Combine $9x^{2}$ and $-10x^{2}$ to get $-x^{2}$.

$$-x^{2}+6x+12+12-6x$$

Add $12$ and $12$ to get $24$.

$$-x^{2}+6x+24-6x$$

Combine $6x$ and $-6x$ to get $0$.

$$-x^{2}+24$$

Differentiate w.r.t. x

$-2x$

Steps Using Derivative Rule for Sum

Combine $9x^{2}$ and $-10x^{2}$ to get $-x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+6x+12+12-6x)$$

Add $12$ and $12$ to get $24$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+6x+24-6x)$$

Combine $6x$ and $-6x$ to get $0$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+24)$$

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 $nax^{n-1}$.

$$2\left(-1\right)x^{2-1}$$

Multiply $2$ times $-1$.

$$-2x^{2-1}$$

Subtract $1$ from $2$.

$$-2x^{1}$$

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

$$-2x$$