Find (d)/(dx)(-7sin(-x)) Answer:

Identify Function: Identify the function to differentiate. We are given the function f(x) = -7sin(-x) and we need to find its derivative with respect to x.Apply Chain Rule: Apply the chain rule for differentiation. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. In this case, the outer function is -7sin(u) and the inner function is u = -x.Differentiate Outer Function: Differentiate the outer function with respect to the inner function. The derivative of -7sin(u) with respect to u is -7cos(u), where u = -x.Differentiate Inner Function: Differentiate the inner function with respect to x. The derivative of u = -x with respect to x is -1.Apply Chain Rule Multiplication: Apply the chain rule by multiplying the derivatives from steps 3 and 4. The derivative of f(x) with respect to x is (-7cos(u)) * (-1), where u = -x.Substitute Back: Substitute u = -x back into the derivative. The derivative of f(x) with respect to x is (-7cos(-x)) * (-1) = 7cos(-x).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find $\frac{d}{d x}(-7 \sin (-x))$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find

\frac{d}{d x}(-7 \sin (-x))

\newline

Answer:

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $f(x) = -7\sin(-x)$ and we need to find its derivative with respect to $x$ .
Apply Chain Rule: Apply the chain rule for differentiation. $\newline$ The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. In this case, the outer function is $-7\sin(u)$ and the inner function is $u = -x$ .
Differentiate Outer Function: Differentiate the outer function with respect to the inner function. $\newline$ The derivative of $-7\sin(u)$ with respect to $u$ is $-7\cos(u)$ , where $u = -x$ .
Differentiate Inner Function: Differentiate the inner function with respect to $x$ . The derivative of $u = -x$ with respect to $x$ is $-1$ .
Apply Chain Rule Multiplication: Apply the chain rule by multiplying the derivatives from steps $3$ and $4$ . The derivative of $f(x)$ with respect to $x$ is $(-7\cos(u)) \cdot (-1)$ , where $u = -x$ .
Substitute Back: Substitute $u = -x$ back into the derivative. $\newline$ The derivative of $f(x)$ with respect to $x$ is $(-7\cos(-x)) \times (-1) = 7\cos(-x)$ .