d/dx(1/2x) = -1/(2x2)
The derivative is 2x based on the power rule. Multiply the power by the coefficient of x then drop the power by one.
-2
d/dx sec(2x) = 2sec(2x)tan(2x)
3x(2x + 1) over (2x - 1)(2x + 1) Cancel out the 2x + 1 Answer: 3x/2x - 1
3
d/dx(1/2x) = -1/(2x2)
3
You are supposed to use the chain rule for this. First step: derivative of root of sin2x is (1 / (2 root of sin 2x)) times the derivative of sin 2x. Second step: derivative of sin 2x is cos 2x times the derivative of 2x. Third step: derivative of 2x is 2. Finally, you need to multiply all the parts together.
Derivative of lnx= (1/x)*(derivative of x) example: Find derivative of ln2x d(ln2x)/dx = (1/2x)*d(2x)/dx = (1/2x)*2===>1/x When the problem is like ln2x^2 or ln-square root of x...., the answer won't come out in form of 1/x.
-2
f(x) = 2/x = 2x^-1 so dy/dx = -2x^-2 = -2/x² f(x) = 2/x This can be re-written as f(x) = 2x^-1 according the to the laws of exponents. Now, we just take the derivative normally: f(x) = 2x^-1 f ' (x) = -1 × 2x^(-1-1) = -2x^-2 The above can be re-written in quotient form as f ' (x) = -2/x²
I'm not sure what you're asking. The derivative of sin(2x^2) is 4xcos(2x^x)dx.The derivative of (sin(2x^2)^2) is 8xsin(2x^2)cos(2x^2)dx.
3
-1
The derivative is 2x based on the power rule. Multiply the power by the coefficient of x then drop the power by one.
It is -2*exp(-2x)