Solve 7 - 4x + 5x ^ 2 - 8 + 7x - 3x | 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

$$7-4x+5x^{2}-8+7x-3x$$

Evaluate

$5x^{2}-1$

Solution Steps

Subtract $8$ from $7$ to get $-1$.

$$-1-4x+5x^{2}+7x-3x$$

Combine $-4x$ and $7x$ to get $3x$.

$$-1+3x+5x^{2}-3x$$

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

$$-1+5x^{2}$$

Differentiate w.r.t. x

$10x$

Steps Using Derivative Rule for Sum

Subtract $8$ from $7$ to get $-1$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-1-4x+5x^{2}+7x-3x)$$

Combine $-4x$ and $7x$ to get $3x$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-1+3x+5x^{2}-3x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-1+5x^{2})$$

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 $nax^{n-1}$.

$$2\times 5x^{2-1}$$

Multiply $2$ times $5$.

$$10x^{2-1}$$

Subtract $1$ from $2$.

$$10x^{1}$$

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

$$10x$$