Maths Calculus
posted by Yousef .
Find the first derivative for the following functions
1) x^3 . sqrt( 3x^5 + 1 ) . sin (7x)

we can rewrite this as
sqrt(x^6)*sqrt(3x^5 + 1)*sin(7x)
sqrt(3x^11 + x^6)*sin(7x)
(3x^11 + x^6)^(1/2) * sin(7x)
then recall that derivative of two functions of x that are multiplied is equal to,
d/dx ( f(x)*g(x) ) = f'(x)g(x) + f(x)g'(x)
therefore,
(1/2)*(33x^10 + 6x^5)*(3x^11 + x^6)^(1/2)*(sin 7x) + (3x^11 + x^6)^(1/2)*(7 cos 7x)
hope this helps~ :) 
thank u so much
helped me alot!!!!! 
dude i love ur name :D
Respond to this Question
Similar Questions

Calculus
Please look at my work below: Solve the initialvalue problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/ Sqrt(4^24(1)(6)))/2(1) r=(16 +/ Sqrt(8)) r=8 +/ Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2 … 
Trig
Find the exact values of the six trigonometric functions 0 if the terminal side of 0 in standard position contains the points(5,4). (0 is not the number zero I don't know what its called) I have to find r first. r=sqrt x^2+y^2 r=sqrt … 
calculus
Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative 
Calculus
Find the derivative of cos(sqrt(e^(x^3)cos(x)) I got sin(sqrt(e^(x^3)cos(x))*((sqrt(e^(x^3)cos(x)) Do I just leave the e^(x^3)cosx alone since it's "e" or do I still have the find the derivative for it? 
Maths  Calculus
Can anyone help with this...I need to find the derivative of the functions below. If possible please show working so I can try and understand? 
Maths  Calculus
Can anyone help with this...I need to find the derivative of the functions below. If possible please show working so I can try and understand? 
Calculus 12th grade (double check my work please)
1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.2 sin 2x B.2 sin 2x / sinh 3y C.2/3tan (2x/3y) D.2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) … 
Maths Calculus Derivatives
Find the first derivative for the following functions 1) f(x) = sin(cos^2x) cos(sin^3x) 2) f(x) = ( tan 2x  tan x ) / ( 1 + tan x tan 2x ) 3) f(x) = sin { tan ( sqrt x^3 + 6 ) } 4) f(x) = {sec^2(100x)  tan^2(100x)} / x 
calculus
Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x. Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative. Use the results … 
Calculus
1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^1 x is 1/(x*sqrt(x^2 1)). …