Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

122,378 users

Calculus Differentiate Help?

0 votes
1. y = 4^x * sin x

2. y = 1 / sin^2 (3x)

Find dy/dx
asked Mar 11, 2013 in CALCULUS by linda Scholar

2 Answers

0 votes

y = 4x × sin x

Diferenciate each side with respective x

dy /dx = d /dx (4x × sin x)

Put f(x) = 4x and g(x) = sin x

Diferenciate each side with respective x for f(x) and g(x)

f(x) = ax then f1(x) = axloga and g(x) = sin x then g1(x) = cos(x)

Therefore f1(x) = 4^x log4 and g1(x) = cos x

Recall : d /dx [f(x) g(x)] = f(x) g1(x) + f1(x) g(x)

Substitute f(x) = 4x ,g(x) = sin x , f1(x) = 4xog4, g1(x) = cos x and  y = f(x) g(x)

dy /dx = d /dx[4x ×sin x] = 4xcos x + 4xlog4 × sin x

dy /dx = d / dx[4x × sin x] = 4x[cos x + 2sin x log2]

Therefore dy /dx = 4x [cos x + 2sin x log2]

answered Mar 11, 2013 by diane Scholar
0 votes

y = 1 / sin2 (3x)

Recall : csc2 (A) = 1 / sin2 (A)

y = csc2(3x)

Diferenciate each side with respective x

dy /dx = d / dx (csc2(3x)

Recall : d /dx (xn) = n(xn-1) and d / dx (cscx) = -cscx cotx

dy / dx = 2csc2-1(3x) 3 [-csc(3x) cot(3x)]

dy /dx = -6csc1(3x)[csc(3x) cot(3x)]

dy /dx = -6 csc2(3x) cot(3x)

answered Mar 11, 2013 by diane Scholar

Related questions

asked Nov 14, 2014 in CALCULUS by anonymous
asked Nov 13, 2014 in CALCULUS by anonymous
asked Nov 12, 2014 in CALCULUS by anonymous
asked Nov 3, 2014 in CALCULUS by anonymous
asked Oct 30, 2014 in CALCULUS by anonymous
asked Oct 21, 2014 in CALCULUS by anonymous
asked Oct 1, 2014 in CALCULUS by anonymous
asked Aug 22, 2014 in CALCULUS by anonymous
asked Mar 4, 2015 in CALCULUS by anonymous
asked Feb 19, 2015 in CALCULUS by anonymous
...