Solve - x ^ 4 - 3y + x ^ 4 + 2y - 5 + 3y | 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

$$-x^{4}-3y+x^{4}+2y-5+3y$$

Evaluate

$2y-5$

Solution Steps

Combine $-3y$ and $2y$ to get $-y$.

$$-x^{4}-y+x^{4}-5+3y$$

Combine $-y$ and $3y$ to get $2y$.

$$-x^{4}+2y+x^{4}-5$$

Combine $-x^{4}$ and $x^{4}$ to get $0$.

$$2y-5$$

Differentiate w.r.t. y

$2$

Steps Using Derivative Rule for Sum

Combine $-3y$ and $2y$ to get $-y$.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-x^{4}-y+x^{4}-5+3y)$$

Combine $-y$ and $3y$ to get $2y$.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-x^{4}+2y+x^{4}-5)$$

Combine $-x^{4}$ and $x^{4}$ to get $0$.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y-5)$$

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 $nax^{n-1}$.

$$2y^{1-1}$$

Subtract $1$ from $1$.

$$2y^{0}$$

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

$$2\times 1$$

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

$$2$$