Find (d)/(dx)(-5cos(7x-1)) Answer:

Identify function: Identify the function to differentiate. We are given the function f(x) = -5cos(7x-1) 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 -5cos(u) and the inner function is u = 7x-1.Differentiate outer function: Differentiate the outer function with respect to the inner function. The derivative of -5cos(u) with respect to u is 5sin(u), because the derivative of cos(u) is -sin(u) and we have a constant multiplier of -5.Differentiate inner function: Differentiate the inner function with respect to x. The derivative of u = 7x-1 with respect to x is 7, because the derivative of a constant is 0 and the derivative of 7x with respect to x is 7.Apply chain rule multiplication: Apply the chain rule by multiplying the derivatives from Step 3 and Step 4. The derivative of f(x) with respect to x is the product of the derivatives from Step 3 and Step 4, which is 5sin(7x-1) * 7.Simplify expression: Simplify the expression. Multiplying 5 by 7 gives us 35, so the derivative of f(x) with respect to x is 35sin(7x-1).

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Find $\frac{d}{d x}(-5 \cos (7 x-1))$ $\newline$ Answer:

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Q. Find

\frac{d}{d x}(-5 \cos (7 x-1))

\newline

Answer:

Identify function: Identify the function to differentiate. $\newline$ We are given the function $f(x) = -5\cos(7x-1)$ 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 $-5\cos(u)$ and the inner function is $u = 7x-1$ .
Differentiate outer function: Differentiate the outer function with respect to the inner function. $\newline$ The derivative of $-5\cos(u)$ with respect to $u$ is $5\sin(u)$ , because the derivative of $\cos(u)$ is $-\sin(u)$ and we have a constant multiplier of $-5$ .
Differentiate inner function: Differentiate the inner function with respect to $x$ . The derivative of $u = 7x-1$ with respect to $x$ is $7$ , because the derivative of a constant is $0$ and the derivative of $7x$ with respect to $x$ is $7$ .
Apply chain rule multiplication: Apply the chain rule by multiplying the derivatives from Step $3$ and Step $4$ . $\newline$ The derivative of $f(x)$ with respect to $x$ is the product of the derivatives from Step $3$ and Step $4$ , which is $5\sin(7x-1) \times 7$ .
Simplify expression: Simplify the expression. $\newline$ Multiplying $5$ by $7$ gives us $35$ , so the derivative of $f(x)$ with respect to $x$ is $35\sin(7x-1)$ .