Solve (x ^ 2 - 3x + 5) + (3x ^ 2 + 3x - 10) | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$(x^{2}-3x+5)+(3x^{2}+3x-10)$$

Evaluate

$4x^{2}-5$

Solution Steps

Combine $x^{2}$ and $3x^{2}$ to get $4x^{2}$.

$$4x^{2}-3x+5+3x-10$$

Combine $-3x$ and $3x$ to get $0$.

$$4x^{2}+5-10$$

Subtract $10$ from $5$ to get $-5$.

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

Differentiate w.r.t. x

$8x$

Steps Using Derivative Rule for Sum

Combine $x^{2}$ and $3x^{2}$ to get $4x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}-3x+5+3x-10)$$

Combine $-3x$ and $3x$ to get $0$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}+5-10)$$

Subtract $10$ from $5$ to get $-5$.

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

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 $nax^{n-1}$.

$$2\times 4x^{2-1}$$

Multiply $2$ times $4$.

$$8x^{2-1}$$

Subtract $1$ from $2$.

$$8x^{1}$$

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

$$8x$$