Differentiate the following expressions with respect to x: (i) y= (2x³-4) X+1 y = x-1 (ii) (iv) f(x)=(x³-3x)(2x²+3x+5) x²+2x y = x 3-x²-2x (v) y= x²-1 y y= √√x(√x+3) Complete Table 2.5 and then, find their derivatives. Table 2.5 (all) y = f(g(x)) (i) y= (6x-5)4 (ii) 1 y= (ii) y=√x²-1 u = g(x) y = f(u) Ic. (iv) y = csc³ x (v) y= 2 Find the derivatives for the following functions: (i) y² = x³ fir 1-xy=x-y y = x² + y² = 2-4x+6y+9 -2 = x²y + y²x ✓ y = and x = t2+1 (vi) x = 2t³ and y = ++++ t3-1 • 3 Evaluate the derivative of f(x) = x3-4 at (-1,-) Differentiation of Trigonometric, Hyperbolic, Logarithmic and Exponential Functions Find the derivatives for the following expressions: (i) Prove that derivative of cot(e) (ii) y = cos(x³+2x-2) is csc² y = x sinx (iv) y = In[sin x] | y= [sinh(x2 – 3) (vi) y = In(cosh x) (vii) y = x sinh x – cosh x (viii) y=In tanh - (ix) y = esinhx (x) for 1(x) = x² tan f(x)=37-sec³ (2x). at (0,36) (xi) f(t) = ecost 2 1-3
Differentiate the following expressions with respect to x: (i) y= (2x³-4) X+1 y = x-1 (ii) (iv) f(x)=(x³-3x)(2x²+3x+5) x²+2x y = x 3-x²-2x (v) y= x²-1 y y= √√x(√x+3) Complete Table 2.5 and then, find their derivatives. Table 2.5 (all) y = f(g(x)) (i) y= (6x-5)4 (ii) 1 y= (ii) y=√x²-1 u = g(x) y = f(u) Ic. (iv) y = csc³ x (v) y= 2 Find the derivatives for the following functions: (i) y² = x³ fir 1-xy=x-y y = x² + y² = 2-4x+6y+9 -2 = x²y + y²x ✓ y = and x = t2+1 (vi) x = 2t³ and y = ++++ t3-1 • 3 Evaluate the derivative of f(x) = x3-4 at (-1,-) Differentiation of Trigonometric, Hyperbolic, Logarithmic and Exponential Functions Find the derivatives for the following expressions: (i) Prove that derivative of cot(e) (ii) y = cos(x³+2x-2) is csc² y = x sinx (iv) y = In[sin x] | y= [sinh(x2 – 3) (vi) y = In(cosh x) (vii) y = x sinh x – cosh x (viii) y=In tanh - (ix) y = esinhx (x) for 1(x) = x² tan f(x)=37-sec³ (2x). at (0,36) (xi) f(t) = ecost 2 1-3
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Differentiate the following expressions with respect to x:
(i)
y= (2x³-4)
X+1
y =
x-1
(ii)
(iv)
f(x)=(x³-3x)(2x²+3x+5)
x²+2x
y =
x
3-x²-2x
(v)
y=
x²-1
y
y= √√x(√x+3)
Complete Table 2.5 and then, find their derivatives.
Table 2.5 (all)
y = f(g(x))
(i) y= (6x-5)4
(ii)
1
y=
(ii)
y=√x²-1
u = g(x)
y = f(u)
![Ic.
(iv) y = csc³ x
(v)
y=
2
Find the derivatives for the following functions:
(i)
y² = x³
fir 1-xy=x-y
y = x² + y² =
2-4x+6y+9
-2 = x²y + y²x
✓ y = and x =
t2+1
(vi)
x = 2t³ and y = ++++
t3-1
•
3
Evaluate the derivative of f(x) = x3-4 at (-1,-)
Differentiation of Trigonometric, Hyperbolic, Logarithmic and
Exponential Functions
Find the derivatives for the following expressions:
(i)
Prove that derivative of cot(e)
(ii)
y = cos(x³+2x-2)
is csc²
y = x sinx
(iv)
y = In[sin x]
| y= [sinh(x2 – 3)
(vi)
y = In(cosh x)
(vii) y = x sinh x – cosh x
(viii)
y=In tanh -
(ix)
y = esinhx
(x)
for 1(x) = x² tan
f(x)=37-sec³ (2x).
at (0,36)
(xi) f(t) =
ecost 2
1-3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00cfc4f8-4666-44f6-b84e-945dea466b0e%2Fc3b62c54-1d43-4da7-8218-cf4a12c55428%2Fcfb4ooi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ic.
(iv) y = csc³ x
(v)
y=
2
Find the derivatives for the following functions:
(i)
y² = x³
fir 1-xy=x-y
y = x² + y² =
2-4x+6y+9
-2 = x²y + y²x
✓ y = and x =
t2+1
(vi)
x = 2t³ and y = ++++
t3-1
•
3
Evaluate the derivative of f(x) = x3-4 at (-1,-)
Differentiation of Trigonometric, Hyperbolic, Logarithmic and
Exponential Functions
Find the derivatives for the following expressions:
(i)
Prove that derivative of cot(e)
(ii)
y = cos(x³+2x-2)
is csc²
y = x sinx
(iv)
y = In[sin x]
| y= [sinh(x2 – 3)
(vi)
y = In(cosh x)
(vii) y = x sinh x – cosh x
(viii)
y=In tanh -
(ix)
y = esinhx
(x)
for 1(x) = x² tan
f(x)=37-sec³ (2x).
at (0,36)
(xi) f(t) =
ecost 2
1-3
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