in the direction of the line (X-31/10 Q4/ Using chain rule to find dw/dt if wrxy-2, X" cost, yesint and zet Q5/ show that fxy=fyx Rxy)= e*y?-x³1Iny

Q: Suppose the slope of the tangent lir

A: Given that the slope of the tangent line at any point on a curve is…

Q: Find the derivative of y = arctan(1 + e²x). О 1 yl= 1+(1+e²)² О 1+e2x yl= ○ yl= 1+(1+e²x)² e2x 2…

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Q: - If W = xy + y2+1 azw Show that a2w ey %3D дхду дудх

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Q: The Power Chain Rule simplifies computing the derivative of a powerof an expression

A: To find the derivative of a power of an expression using the chain rule. ddxe3x+1 Solution: Chain…

Q: 3. f(t) = -2t2 + 3t – 6 6. h(s) = s4/5 1 +1 9. h(t) = 1* + 21 + 2

A: To find the derivative of f(t)=-2t2+3t-6, use the power rule of differentiation, ddttn=ntn-1.

Q: Find yy as a function of x if y′′′−7y′′+12y′=6e^x y(0)=30,  y′(0)=19,  y′′(0)=12

A: y′′′−7y′′+12y′=6ex        y(0)=30,  y′(0)=19,  y′′(0)=12 given differential equations is linear…

Q: Given the following initial value problem dy (1+ x)/(y) with y(0)=1 dr Find y(0.4) by using…

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Q: Q/ show that f(Z) = |Z|2= x² + y² has a derivative only at the origin

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Q: Find y' if y = In(7x² ? + 3y2). бу 7 + 3y y'

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Q: In the derivative, transform into linear equation y = mx + b (the form)

A: Given :  y = mx + b (the form)   To find : In the derivative, transform into linear equation

Q: Find y' if y = (26 +1)18z+6 y' = (18z + 6)(z6 +1)18z+5(6z5) y' = (z6 + 1)18z+6 18(6)z5 26+1 y/ = (26…

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Q: of y = 2 tan x 1-tan²x

A: Solution is done in step 2

Q: Differentiate the function. fx) = (4 +x*)° - (1+x*) %3D f'(X) =

A: We have to find derivative

Q: Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.

A: Given differential equation     x2y'=y   and initial condition  at x=1,y=2/e

Q: y" = 2y^3 + 8y, where y = 2; y'= -8 when x = 4

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Q: 2 3^ 2^ 7. IF A = x²y²² - 2x²²³3 + x²³² k B = 2zi+yj-x²2 FIND ² axay À X B = (AXB) @ POINT (1,0, -2)

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Q: Use the Chain Rule to find 2 when and r = 2se', y = 1+ set.

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Q: Find y' (x) if (3xy +7)² = 6y.

A: Differentiate both sides with respect to x and by using the formula for derivative of square of…