EXAMPLE 3 Derivative rules Compute the following derivatives, where u(t) = ti + ťj –- tk and v(t) = sin t i + 2 cos tj + cos t k. d b. 뜻(12 v(t)) d c. 7(u(t) • v(t)) a. dt

Q: 4. Find using derivative rules. dx sinx x8+x x2 tanx (a) y = (b) y= (c) y = cos³(3x² + 9) cos(5 x*)…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: 2. Answer the following derivative related questions. dy. (1) Let y = x' + 4x³ + 2x² + 16, find ; dx…

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Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. 29 de ²4 (2t5 - t) ²9…

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Q: 2.) Compute for the derivative (DO NOT USE THE DEFINITION) of A. 2x3 y = tanh sin x2

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Q: Find the derivative of y with respect to x. y= tan 2x 3 9 OA. 4x²+9 毒 6 О в. 4x²+ +9 -6 ○ C. 4x²+9 2…

A: y=tan−1(32x​)We can find the derivative of the function using the chain rule. The chain rule states…

Q: compute the derivative. r(1) = (7 – 1, 4 ī, 8)

A: The given function is rt=7-t,4t,8.

Q: Find the derivative of the function at the given point in the direction of A. f(x, y) = -10x2 + 5y,…

A: This question is related to directional derivative of a function, we will solve it by finding…

Q: Write a chain rule formula for the following derivative. dw for w f(p,q); p= g(x,), q = h(,) O A. aw…

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Q: . Does the function cos x x + 0 f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A: Consider the given function fx=1-cosxx        x is not equal to 0x=0

Q: Calculate the derivative. (Use symbolic notation and fractions where needed.) d sec(2x – 5) dx = 100

A: we have to calculate the derivative using fundamental theorem of calculus

Q: Which is the derivative (dy/dx) of y=sin-1 tanx?

A: Formula used   (fog)'(x) = f'(g(x))*g'(x)

Q: compute the derivative : y = cos(cos(cos(θ)))

A: the given function is: y=coscoscosθ we have to find the derivative of the given function.

Q: compute the derivative. y = z csc(9z + 1)

A: y=z csc9z+1

Q: Theorem 1: Constant Rules Let y = c for any real number c, then dy d dx lc] = 0 That is the…

A: Given that: y=c and y'=0

Q: Use the Fundamental Theorem of Calculus to find the derivative of cos t dt t8 y = [NOTE: Enter a…

A: The given function,y=∫-9xcos tt8dt