More Derivatives

Chain Rule

100

The derivative of y=(4x)⁴/16 using chain rule

What is (4x)³

200

The derivative of y=2(100-7x)³ using chain rule

What is -42(100-7x)² ?

300

The derivative of f(t)=(1/(t-3))² using chain rule

What is -2/(t-3)³ ?

400

The derivative of y=4sec²(x) using chain rule

What is 8sec²(x)tan(x) ?

500

The derivative of y=sin³(x²) using chain rule

What is 6xsin²(x²)cos(x²) ?

Implicit Differentiation

100

dy/dx of x²+y²=9 using implicit differentiation

What is dy/dx=-x/y ?

200

dy/dx of 2x³+3y³=64 implicit differentiation 

What is dy/dx= -2x²/3y² ?

300

dy/dx of x³-xy+y²=7 using implicit differentiation 

What is dy/dx=y-3x²/2y-x?

400

dy/dx of sin(x)+2cos(2y)=1 using implicit differentiation 

What is dy/dx=cos(x)/4sin(2y) ?

500

dy/dx of x=sec(1/y) using implicit differentiation 

What is dy/dx=-y²/sec(1/y)tan(1/y)?

Log. Differentiation

100

dy/dx of y=x/(x+1) using logarithmic differentiation

What is dy/dx=1/(x+1)² ?

200

dy/dx of y=x^x-1 using logarithmic differentiation

What is dy/dx=(lnx+1-x^-1)x^x-1?

300

dy/dx of y=x(x²+1) using logarithmic differentiation

What is dy/dx=(2x²+1)/(x²+1)^1/2 ?

400

dy/dx of y=x^2/x using logarithmic differentiation

What is dy/dx= 2(1-lnx)x^(2/x)-2?

500

dy/dx of y=x^lnx using logarithmic differentiation

(2x^lnxlnx)/x