Write a chain rule formula for the following derivative. du for u= f(p,q); p=g(x,y,z), q = h(x,y.z)

Q: Use an appropriate form of the chain rule to find the derivative. R = e3s=t"; 3s-t2 s = 4ø, t= $/2…

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Q: 1. Find the derivative of the following functions. 1 (b) y(t) = Vi (c) y(t) = - (a) y(t) = t %3D

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Q: Use an appropriate form of the chain rule to find the derivative. R = e8s-t; s = 4¢, t= ¢/2 dR dø ||

A: Given: Now,         dRdϕ=∂R∂sdsdϕ+∂R∂tdtdϕ      =e8s-t2· 8dsdϕ+-2e8s-t2tdtdϕ      =e8s-t2·…

Q: find fxx(x,y) and fxy(x,y) derivatives for the following function z=f(x,y)= e^x^2 +y^2

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Q: Use an appropriate form of the chain rule to find the derivative. R = e8s-t. = 4ø, t= ¢'/2 S dR dø…

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Q: Find the derivative of the function j(x), below. Assume that c and d are constants. j(x) = In(e" +…

A: answer of given question is in step 2

Q: Find the derivative of the function. g(u) =√u+1(1 − 5u2)7

A: Write g(u) using exponent

Q: The directional derivative of f(x, y) = -2e" cos y at (0, ") in the direction of v = (-6, 8) is O 7…

A: GIVEN : f(x, y) = -2 ex cosy     at  (0, π4)                in the direction of v = (-6, 8)

Q: Let v(t) = (t, - 2t,7). Compute the derivative of the following function. v(e')

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Q: Find the derivative of y with respect to the independent variable. 6- e y=t O A. (6- ers-e O B. (5-…

A: The derivative of xn is given as,ddx(xn)=nxn-1

Q: Use the chain rule to compute the derivatives. a) f(x) = sin? x = (sin x)? b) f(x) = sin(x²) c) f(x)…

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Q: 2. If u3 = a³t, find· d?u where a is a constant. dt2

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Q: Find the derivatives of f(x)=(ax4+b)6   and   f(x)=axe-bx+15 Assume that a and b are constants.

A: Given query is to find the derivative of the expression.

Q: Find the given higher-order derivative. f (4)(t) = t cos t, f (5)(t)

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Q: Use this definition to compute the derivative of the function at the given value. g(t) = t = 4 %3D…

A: g(t)=tt+1,  t=4

Q: Find the derivatives of the following functions. F(z) = 3 + cos(2z −1

A: Given :   f(z) = 3+cos2z-1

Q: Let v(t) = (, - 41,3). Compute the derivative of the following function. v(e')

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Q: Find the derivative of the function at P, in the direction of u. x- 3y g(x.y) = 2хy +3 Ро(1, - 1),…

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Q: Find the derivative of v(t) = t5e-d Assume that c is a constant. v (t) =

A: Topic = Derivative

Q: Let y = (x + sin(x))³. Find g(æ) and f(x) so that y = (f o g)(x), and compute the derivative using…

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

A: for the partial derivative of w w.r.t x ,  First we will partial derivate w w.r.t. p and then p…

Q: Find the directional derivative of the function at the point P in the direction of the p f(x, y) =…

A: Directional derivative of f in dircetion of u is given by=  (grad f).u Here we first calculate…

Q: Find the derivative of y with respect to x. 6х + 11 y = - csc 7 O A. 42 |6x + 11|V(6x + 11)2 – 49 O…

A: ddx(cosec-1x)=-1xx2-1

Q: Let v(t) = (t², -4t,9). Compute the derivative of the following function. v(e¹)

A: Solve the following

Q: Find the derivative of v(t)=(t^9)e^(-ct) Assume that c is a constant. v′(t)=

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Q: Find the relation of the derivative of y and y with respect to x, given that yx-y? = 3x 3x II. 1-2xy…

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Q: Use the Chain Rule to find the derivative of the function. y = (x + Sx?)-1

A: Derivative of function

Q: Write a chain rule formula for the following derivative. for u = f(p, q); p = g(x, y, z), q = h(x,…

A: Given problem:-

Q: compute the derivative. g(t) = e4t−t2

A: The derivative of a function is given by the expression f'(x)=limh→0f(x+h)-f(x)h. For some standard…

Q: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6, 8) is 14 O…

A: Here,

Q: 1. y u? +1; u= 3x -2 2. y =u2 + u -2; u= 2 %3D

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Q: Use an appropriate form of the chain rule to find the derivative. R = e5s-t; s = 5¢, t = 6/2 %3D dR…

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Q: Find the derivatives of the functions s =√t/1 + √t

A: The function is s=t1+t.   Differentiate the function with respect to t.…

Q: Find the following derivatives of f(x,y) =2yey. f,x, y) = ,6, 9) =| fa(x, y) = fylx, y) = %3!

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Q: compute the derivative of r(t) = (t, t8,t12)

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Q: Use an appropriate form of the chain rule to find the derivative. R= e5s-t. s = 80, t= ¢!/2 %3D dR…

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Q: Find the derivative of the function. G(z) = (1 – 3z)2V z? + 1 G'(z) =

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Q: A) F(u) - u' + tu +1 . 4u +1 = 2 B) 2 c) h(m)=2I h(u) - 3e+I %3D

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Q: For each function below, find the derivative using the Chain Rule. If h(z) = 2(2x² + 3)", then h'(x)…

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Q: Use an appropriate form of the chain rule to find the derivative. R= e28-t; s = 80, t /2 %3D dR %3D…

A: Given R=e2s-t2 Where s=8∅,t=∅1/2 we need to calculate the value of drd∅ drd∅=dd∅(e2s-t2)…

Q: compute the derivative g(t) = e4t−t2

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Q: I) Find the derivative of each function a)y =x' In x b)y = 4x'e c)y = eF

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Q: 1. y = u=x? + 1 2. y= www v 3. y3D u? + 2u -3; u = Vx

A: We have to find derivative y by using chain rule.

Q: Use an appropriate form of the chain rule to find the derivative. R = e7s-t; s = 9ø, t= $/2 dR dø

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Q: Calculate the derivative of y = /x+ If the Chain Rule only needs to be used once, which functions…

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Q: (c) Use the chain rule to find the derivative of the function z = 2r*y³ – ry² along the curve given…

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Q: Find the derivative of the function at P, in the direction of A. f(x,y) = 4xy + 2y, Po(4, - 4), A =…

A: Derivative of a function f(x,y)  at (x0,y0) in the direction of a unit vector u^=ai + bj is ,…

Q: Calculate the derivative of the following function. y= /4+ cot?x If the Chain Rule only needs to be…

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Q: Find derivatives of the functions defined as follows:

A: Our Aim is to find the derivative of the function given below:-y=t2 e2ttt+e3t-(i)

Q: Use an appropriate form of the chain rule to find the derivative. R = ebs-t; s = 5¢, t = /2 s = 50,…

A: To use an appropriate form of the chain rule to find the derivative.