The position s of a point (in feet) is given as a function of time t (in seconds). s = -13 + t - 13t2; t = 2 (a) Find the point's acceleration as a function of t. s"(t) = ft/sec? (b) Find the point's acceleration at the specified time. s"(2) = ft/sec2

Q: Find the derivative of the function. 7x-4 y = 6x + 1

A: Giveny=7x-46x+1We know thaty'=ddxf(x)g(x)=f'(x)g(x)-g'(x)f(x)g(x)2

Q: Find an equation of the line that is tangent to the graph of the function f(x)= 2x and parallel to…

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Q: Find the slope m of the line tangent to the graph of the function f(x)=9-x^2 at point P(4,-7).

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Q: Find the derivative of the function.     y = 5(2 − x3)4

A: We use the power rule and the chain rule

Q: Find the derivative of the function.

A: We have to find the derivative of the given function   The given function is

Q: Find the derivative of the function. y = (2x – 5)*(8x² – 5)-3

A: Derivative denotes rate of change. According to product rule, ddxf(x)g(x)=ddxf(x)g(x)+ddxg(x)f(x)

Q: Find the derivative of the function. 4x +7 y = 3

A: Quotient rule: ddxfxgx=gxddxfx-fxddxgxgx2

Q: HOW DO YOU FIND THE DERIVATIVE OF THE FUNCTION?y=(7X(CUBED) PLUS 2X)TO THE SIXTH POWER

A: Initial Calculation:The variable y is a function of x. The derivative of y found with respect to x…

Q: Find the equation of the line tangent to the graph defined by the equation at the point (2,0).…

A: Given equation of curve ,xey-y=2 -1

Q: Find the slope m of the tangent line to the graph of the function at the given point and determine…

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Q: Find the derivative of the 10 economic functions. Show full solutions and properly name the…

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Q: Find the derivative of the function. y = 3√(6x2 + 1)

A: y=36x2+1

Q: Find the derivative of the function. y = 5x² + 2* + 3

A: The sum rule of differentiation states that ddx(f(x)+g(x))=f'(x)+g'(x). The differentiation of the…

Q: Find the derivative of the function f(x) (3x+6)? 6x2+13

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Q: Find an equation for the line tangent to the graph of  f(x)= 2xex at the point (3,f(3)). y=?

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Q: Find the derivative of the function.

A: Given y=2x-73

Q: x5/2+4 x3 y = 3

A: We have to find the derivative of the given expression: y=x52+4x3x3 Simplifying the given…

Q: Find the derivative of the function. Express the answer using positive exponents only. y = (4x5 –…

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Q: Find the derivative of the function. y = 2  4√(9 − x2)

A: Given function: y=29-x24

Q: Find the derivative, but do not simplify your answer. 2 3 y = (x + x + 4)Vx – 2/x + 7 -

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Q: Find the derivative of the function. y = 10(9 – x2)3

A: Find the derivative of the function y=109-x23.

Q: Find the derivative of the given function.     y=16z2+14z

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Q: 5. Iny+ea²²x+y = 10 -

A: The given equation is lny+ex2y2-x+y=10. Find the derivative of the equation. Here we use the…

Q: Find the derivative of the function. y = (2x − 7)3

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Q: Find the derivative of the function. y=x²- + 35x+9 44 y'-O

A: Given, y = x3 - x2/44 + 35x +9 We will use d(xn)dx = nxn-1                       d(constant)dx = 0

Q: Find the derivative of the function. Express the answer using positive exponents only. y = 2/3x3(4x5…

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Q: find the first and second derivative: x=(t-2)5/2 y=t3-5

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Q: Find the equation of the tangent to the curve y = 2x2 - 5x + 3, where x = 2.

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Q: I need help with finding the derivative.  y=(2x^2   +   1)^2   (x-1)^3

A: Given: y=2x2+12x-13 We know that ddxu.v=vdudx+udvdx…

Q: b) Write an equation of the tangent line to the curve x² + y - 25 = 0 at the point (3,4).

A: To find an equation of tangent line to the curve x^2+y^2-25=0 at point (3,4).

Q: Q#2. By definition find derivative of (2x+3)/4.

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Q: Calculate the derivative of the function y=(2−x3)(13+x2).

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Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

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Q: Find the derivative of the function y=3√2x2.

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Q: Find equations of the two tangent lines to the graph of f(x) = that pass through the point (-1, -3).…

A: Let the point on the curve c,c2 on the curve through which the tangent line passes, As we know that…

Q: Find the equation of the line tangent to the graph f(x) = – at the point (4,1).

A: Given:            fx=4x To find the slope of the tangent line, find the value of the derivative of…

Q: Find the derivative 3 y = 2 + Væ4

A: To find the derivative of the given function y=3x+x43 we use power rule of derivative. Power rule of…

Q: Find the equation of the line tangent to the graph of f(x) = x² + = - 9 at x = 7. y = help…

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Q: Find the derivative of the function y=(2x+5)^4(3x+1)^-5

A: The given function is y=(2x+5)4(3x+1)-5. The negative property of exponent isa-x is 1ax. The…

Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: Find the derivative of the function. y = 1/(x2 + 5)3

A: Solution:- The given function is  y=1(x2+5)3

Q: 2x + 9y = 6x?y – 5æ3

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Q: Find the derivative of the functionG(y)=(y^2/(y+2)^3

A: Apply quotient rule for differentiation

Q: Find the slope and an equation of the tangent line to th 3 2 3. f(x) = + 8x + 8; (-1, 21 slope 11…

A: Recall: Point-slope intercept form :  y-y1 =m x-x1 where , 'm=dydx' is the slope and x1,y1 are given…

Q: Calculate up to 3rd derivative the equation f(x) = 5x²(x+ 47)

A: We have to find the 1st,2nd,and 3rd derivative of the given function.

Q: The equation of a curve is y= 4x²+4lx+12-k, where kis a constant. In the case where k=1, find the…

A: If a line is parallel to the x-axis then its slope will be 0.   Slope of the curve y=f(x) is m =…

Q: Find the derivative of the function f(x) = x2 -8x +9 at the number a

A: The given equation is f(x)=x2-8x+9 The derivative of the function is the rate of the change in the…

Q: Find the derivative of the function (2а — 5) (5ӕ — 4) - f(æ) : 9x2 – 2 f'(x) =

A: The objective of the question is determine the derivative of the given function.

Q: 13: 3. y = V(4x + 3)3

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.