Differentiate y= (6x^2 - 5)^(3/2) with respect to x
Simplify the equation to y=u3/2 where u = 6x2 -5Use the chain ruledy/dx = dy/du x du/dxdy/du = (3/2)u1/2du/dx = 12x - 0Therefore dy/dx = (3/2)u1/2 x 12xBut u = 6x2-5 so substitute that into the derivative.dy/dx = 3/2(6x2-5)1/2 x 12xSimplify to dy/dx= 18x(6x2-5)1/2
Related Maths A Level answers
All answers ▸Consider the closed curve between 0 <= theta < 2pi given by r(theta) = 6 + alpha sin theta, where alpha is some real constant strictly between 0 and 6. The area in this closed curve is 97pi/2. Calculate the value of alpha.
Integrate sinx*ln(cosx) with respect to x.
The line L1 has vector equation, L1 = ( 6, 1 ,-1 ) + λ ( 2, 1, 0). The line L2 passes through the points (2, 3, −1) and (4, −1, 1). i) find vector equation of L2 ii)show L2 and L1 are perpendicular.
Find the gradient of the curve y = sin(2x) + 3 at the point where x = pi