AP Physics Summer HW

Derivative sin(x)

cos(x)

Derivative cos(x)

-sin(x)

Derivative tan(x)

sec²(x)

Derivative cot(x)

-csc²(x)

Derivative sec(x)

sec(x)*tan(x)

Derivative csc(x)

-csc(x)*cot(x)

Differentiating sin(3x) using chain rule

3cos(3x)

Derivative e^x

e^x

Derivative a^x

a^x*ln(a)

Derivative ln(x)

1/x

Derivative e^u(x)

e^u(x) * u’(x)

Derivative a^u(x)

a^u(x) * ln(a) * u’(x)

Both base and exponent are variable (x^x, x^sinx)

1. Take natural log:

   1. ln(y) = xln(x) for y=x

2. Differentiate implicitly

   1. y’/y = derivative(xln(x))

3. Solve for y’

   1. y’ = y*(lnx + 1) = x^x(lnx+1)

Derivative y = x^x

y’ = x^x(lnx+1)

Derivative x^sinx

y’ = x^sinx [cosx * lnx + (sinx/x)]

Where i left off

Derivatives of Exponential Functions & Logarithmic Differentiation Calculus lnx, e2x, xx, xsinx