Derivatives of... 1.y=cos^2(3x^2+7x) 2. Y=ln(tan^-1(3x)) 3. Y=(x^3+2^x)sin(x) 4.

Question

Derivatives of... 1.y=cos^2(3x^2+7x) 2. Y=ln(tan^-1(3x)) 3. Y=(x^3+2^x)sin(x) 4. Y=(sin(3x))/(ln(2x)) Use implicit differentiation 1. Xy=sin(x+y)+42^y 2. Tan(x+y^8)=sin^-1(x^2+y) Use logarithmic differentiation on the following: 1.y=(x^3cos(3x+5))/((x^2+3x+4)^42) 2. Y=x^(sin^-1(3x))
Find the tangent line to the curve y=x^4-3x^2+12 that passes through the x-coordinate (Two, 16).
Find the points to the curve y=x^3-3x-4 where the tangent line is horizontal. Derivatives of... 1.y=cos^2(3x^2+7x) 2. Y=ln(tan^-1(3x)) 3. Y=(x^3+2^x)sin(x) 4. Y=(sin(3x))/(ln(2x)) Use implicit differentiation 1. Xy=sin(x+y)+42^y 2. Tan(x+y^8)=sin^-1(x^2+y) Use logarithmic differentiation on the following: 1.y=(x^3cos(3x+5))/((x^2+3x+4)^42) 2. Y=x^(sin^-1(3x))
Find the tangent line to the curve y=x^4-3x^2+12 that passes through the x-coordinate (Two, 16).
Find the points to the curve y=x^3-3x-4 where the tangent line is horizontal. 1.y=cos^2(3x^2+7x) 2. Y=ln(tan^-1(3x)) 3. Y=(x^3+2^x)sin(x) 4. Y=(sin(3x))/(ln(2x)) Use implicit differentiation 1. Xy=sin(x+y)+42^y 2. Tan(x+y^8)=sin^-1(x^2+y) Use logarithmic differentiation on the following: 1.y=(x^3cos(3x+5))/((x^2+3x+4)^42) 2. Y=x^(sin^-1(3x))
Find the tangent line to the curve y=x^4-3x^2+12 that passes through the x-coordinate (Two, 16).
Find the points to the curve y=x^3-3x-4 where the tangent line is horizontal.

Explanation / Answer

1.y=cos^2(3x^2+7x)

y' = 2cos(3x^2+7x) (d/dx(cos(3x^2+7x)))

           = -2cos(3x^2+7x).sin(3x^2+7x) (d/dx(3x^2+7x))

            = -2(6x+7)cos(3x^2+7x).sin(3x^2+7x)

2. Y=ln(tan^-1(3x))

y' = (1/(tan^-1(3x)))(d/dx((tan^-1(3x)))

=(1/(tan^-1(3x))) * (1/(1+9x^2))(3)

(3/(1+9x^2))(1/(tan^-1(3x)))

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.