Find the tangential component ar and the normal component an of acceleration as a function of t if r(t) = (2r, 5t) (Express numbers in exact form. Use symbolic notation and fractions where needed.) ar(1) = an (t) =

Q: Compute the derivative of f(t) = (3t2 + sin t, cos3 t + 8t2, 5tan t) relative to t.

A: d(u+v)/dt=  du/dt + dv/dt

Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

Q: Find the value of the derivative of (z – 4i)8 at z = 3 + 4i |

A:

Q: by s-differentiation find L (t cos3t) = %3D s2 (s² +9) s2-3 .b O (s2+3)2 s2 (s²+9)2 s2-9 (s2+9)2

A:

Q: Find the differential of the function. u = 2x5 + 5

A:

Q: Find the derivative. 4 7(+3t) dt 7(P+31)-] 4 dt

A:

Q: find the partial derivative of the function withrespect to each variable.35. ƒ(t, a) = cos (2pit -…

A: The given question is taken from the partial derivative in which we have to find the partial…

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

Q: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: 3. Find the derivative of the function f(x, y, z) = xy³ + yz³ + zx³ at the point (-1, 2, 1) in the…

A:

Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: Find the directional derivative of f(x, y) = In(e"- 3y) at the point (0,0) in the direction of 3i +…

A: We are asked to find directional derivatives of function.

Q: 12. Find derivative of the following composite function using the Chain Rule: 2y t(y) = 6y² + 1+y?…

A: We have to find derivative

Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: 1 Find the direction derivative of f(x, y, z) = x²y -zx -y³x at the point (1,-1,1) in the direction…

A: Directional derivative

Q: (a) Find the directional derivative of φ = x2 + sin y −xz in the direction i+ 2j−2k at the point (1,…

A: a) Given that φ=x2+siny-xz Now first evaluate gradient of φ, so…

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: fx=sin-1x,   a=π12 The value of the function and the value of the derivative can be easily…

Q: Find the maximal directional derivative of function f(x,y) = xln(x+y)+x²y at the point (-1,2).…

A: To find -

Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i -3j b)…

A:

Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

A:

Q: 5. Find the gradient of cos(xy) – 3y* + 3 at the point (1,4)

A:

Q: Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the…

A: Given function is, cx=aebx Here, a>0 and it's constant here we have to see the effect of b so,…

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: Find the derivative of the function at Po in the direction of A g(x, y) = x - (y/x) + V3 sec (2ry),…

A: Let us consider the given function z=f(x,y) The directional derivative of the function at Point P in…

Q: Find the differential of the function. u = 5x4 + 7

A: Differentiate wrt x

Q: Find the differential of the function. y = (5 - v^2) / (5 + v^2)

A:

Q: Find the derivative of the function. g(u) = (8+ u²)*(1 – 5u²)8 %3D = (n), 6

A: Now we will differentiate g with respect to  u . And we will  derivative the function using chain…

Q: Find the derivative of the function at P, in the direction of A g(x,v) = x - (y² /x)+ V3 sec (2xy),…

A: Given that  g(x,y)=x-y^2/x+√3arcsec(2xy) P(1,1) and A=12i+5j To find the directional derivative of g

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rcos(r) (3…

A:

Q: Q/1: Find the derivative of the non-uniform B-Spline curve with (k=3, n=5) Basis Functions N2.

A:

Q: Find the normalizing constant c so that ce-x/4 dx = 1. C =

A:

Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

A:

Q: 1. Use the "First Fundamental Theorem Of Calculus" to find the first derivative of the function. 2 –…

A:

Q: 3. Use the Fundamental Theorem of Calculus Part I to find the derivative of a) [(cost +r +e' )dt b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 3. Find the derivative of the function f(r, y, ) = xy + yz+ the direction A = 3i + 6j – 2k. zr at…

A:

Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 6x+10y,…

A:

Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x - (y/x) + V3 sec-…

A: Given problem:-

Q: 10. Use differentiation to find the gradient of the curve y = ax sin(bx) at x = 3. 7. -17 b= 19

A: Please refer to the image below

Q: x²+4 Compute the derivative of the vector-valued function: r(t) = ln- x-5 i+ sin ² tj + (t² + 1)²k

A: Given vector valued function r(t)=lnx2+4x-5i+sin2tj+t2+12k The objective is to compute the…

Q: Find the derivative of the function at the given point in the direction of A. 3) f(x, y, z) = -10x+…

A: Here initially we need to find out the partial derivative of the given function to find out the…

Q: EXERCISES 2: Find the derivative of the function at Po in the direction of A. 1. f(x, y) = 2xy –…

A:

Q: Find the differential of the function. u = 2x + 7 du = %3!

A:

Q: 5. (а) Find the directional derivative of f at P in the direction of ā if f(x,y) = y In(x) ; P(1,4);…

A: To find The directional derivative of f at p in the direction of a.

Q: 9. Find the directional derivative of f(x, y) = 3x² – y² + 5xy at (2,–1) in the direction of -3i –…

A:

Q: Find the directional derivative of w=2x²yz in the direction of v=3i-4j at the point (-1, 1.13)

A:

Q: Find the value of the derivative of 23 1. (z+i)3 2. (z – 4i)8 at z = 3 + 4i at z = i

A: at z=i

Q: Find and using implicit differentiation. az Leave your answers in terms of x, y, z, and w. In(4r² +…

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.