Find dy/dx at the point (0, 1), if y^5 = (x + 2)^4 + e^xln y − 15 Amy.

Differentiate the exponential function

find dy/dx: y=ln(x^2)

find dy/dx: y=cos(x^2)

find dy/dx: y=sin(x^2)

find dy/dx: y=(x^2)/(x-1)

find dy/dx if y=x^4-5x^2+6

Use limits to differentiate f(x)=cos(x)

Differentiate the exponential function

Find the derivative of  the function:

Solution:

Logarithmic differentiation is a very efficient way to evaluate this derivative:

Limit Definition of Derivatives

Use the definition of derivatives to find the derivative of sqrt(x)

Solution:
Multiplying by a conjugate can be a useful strategy and it helps in this problem. We also notice that sqrt(2) is only defined for real numbers greater than or equal to 0 (for calculus). This means the absolute value of an expression is also greater than or equal to 0. In the denominator we must be careful not to multiply because factoring out the delta-x is easier.