Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

Q: Find the derivative of the function by using the rules of differentiation. 4 f(u) = %3D f'(u) =

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Q: Calculate the derivative. d sec(8x + 96) dx = sec(8t+96) dt On what interval is the derivative…

A: From the given problem:   ∫67tsec8x+96dx   Applying the Leibnitz rule:…

Q: Find the gradient of the tangent line to y when x = 2.

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Q: Find the exact slope of the tangent line to sin (x) y = f(x) = 2x + S at the point where x = 2

A: we have the function y=f(x)=2x+sin(x)2 we have to find slope at point x=π6

Q: Use implicit differentiation to find the equation of the tangent line of the curve at the given…

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Q: y = x*lnx %3D %3D

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Q: Find the equation of the tangent line to the curve at the given point using implicit…

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Q: Calculate the derivative using implicit differentiation: ∂w/∂z,x^3w+w^7+wz^2+2yz=0 ∂w/∂z = ?

A: To find the implicit derivative of the given equation.

Q: Use implicit differentiation to find the slope of the tangent line to the curve at the point…

A: Given that  (xy^3)/(1+secy)=1+y^4  To find the slope of the tangent line

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Now slope of the tangent line is the derivative of the given curve at the given point. So…

Q: Use implicit differentiation to find the slope of the tangent line to the curve defined by 3xy + xy:…

A: Given function3xy3+xy=26differentiate wih respective…

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Use implicit differentiation to find the slope of the tangent line to the curve at the point…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: First find the derivative at given point than write the equation of tangent line in slope intercept…

Q: Use the definition of derivative to find the derivative of R(z) %3D

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Q: Use implicit differentiation to find the equation of the tangent line for y+ xy = 6 at the point…

A: The objective is to find the equation of tangent line  at the point (1, 4).

Q: Compute the derivative of f(x) = (sin x)v , 0 < x < T.

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Q: Find the equation of the tangent line to the curve at the given point using implicit…

A: First find the derivative at given point then write the equation of tangent line in slope point…

Q: Calculate the derivative.

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Q: x'+e' = y

A: Given: ⇒x2+ey=y2

Q: Find the derivative of f(x) = (sin a)" %3D

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.

A: As we know that: The expression for the directional derivative  in the direction of a→ is:…

Q: Use implicit differentiation to find the slope of the tangent line to the curve at the point (…

A: The given equation is xy31+secy=1+y4 and point of tangencey is -13, 12 Take derivative on both sides…

Q: Use implicit differentiation to find the slope of the tangent line to the curve y sin2x xcos2y at…

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Q: use implicit differentiation to find out the slop of the tangent line to the curve at the point…

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Q: calculate the derivative with respect to x. sin(x + y) = x + cos y

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Q: Find the directional derivative of f at the given point in the direction indicated by the angle θ.…

A: Given, 4. f(x,y) =xy3 - x2, (1,2) , θ = π/3

Q: Find the derivative of the function. t) 3DV5+ tan t

A: The derivative of the following function needs to be evaluated  f(t) = 5+tant9

Q: Find the directional derivative of f(x, y) = V5x + 3y at the point (0, 2) in the direction 0 3…

A: f(x,y) = 5k+3yt point (0,2)in direction θ= 5π4 radiusto find directional derivativesolution1)…

Q: Compute the derivative with respect to x using differentiation rules.  f(x) = eax cos(bx) for…

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Q: Find the derivative of a linear function y=ax+b using the definition of derivative.

A: The derivative of a function f' of function f is defined as f'x=limh→0fx+h-fhh

Q: Calculate the derivative using implicit differentiation: ∂w/∂z, x^4w+w^3+wz^2+2yz=0 ∂w/∂z=

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Q: Find the gradient of the tangent to the curve y = at the point with x 1. x+1

A: giveny=x2x2+1differentiatey'=(x2+1)2x-x2.2x(x2+1)2=2x(x2+1)2

Q: Find the derivative of function.

A: Use the product rule to find the derivative for s. s=t2lntdsdt=ddtt2×lnt+t2×ddtlnt

Q: Find the gradient of the tangent line to y when x =- 1

A: The explanation of answer as follows

Q: Use implicit differentiation to find the slope of the tangent line to the curve at the point (- 1/3,…

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Q: Find the derivative of f (y) In(y)

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Q: Use implicit differentiation to find the gradient of the tangent line for xy 6xy - 2x = 9 at the…

A: topic- application of derivative

Q: Use implicit differentiation to find an equation of the tangent line to the cardioid at the point…

A: Given function is  x2+y2= (2x2+2y2-x)2  We have to find the equation of tangent at (0,-0.5) .

Q: Calculate the derivative using implicit differentiation: dw x®w+w² + wz² + 2yz = 0 dz' dw dz II

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Q: Use the rules of differentiation to find the derivative of the function. y == cos(e) – cos(0) 2 y' =

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Q: Use implicit differentiation to find the equation of the tangent line to the curve e^y sin(x)+x−xy=π…

A: We have to find the equation of tangent

Q: f(x) = cos vx

A: The derivative is defined as f'(x)=limh→0f(x+h)-f(x)h.

Q: Use implicit differentiation to find the slope of the tangent line to the curve at the point…

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Q: The directional derivative of f(x, y) in the directional

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Q: Find the derivative.

A: Given,

Q: Use implicit differentiation to show that the equation of the tangent line to the curve y²=kx at…

A: Given : y2=kx Therefore, y=k.x  .............................(1) Now, put (x0,y0) in the above…

Q: Find the unit direction vector of greatest decrease of f at xo = [0 - 1 1]' and evaluate the…

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Q: Calculate the gradient of the tangent line to the curve y3 - x3 -xy = 1at the point (-1,0).

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