Derivatives

Power Rule

100

The derivative of the function f(x)=12x³

what is 36x²

200

The derivative of f(x)=(1/2)x^-2

What is -1/x³

300

The derivative of f(x)=3x⁵+8x⁹-15x^-3-x²+5

What is 15x⁴+72x⁸+45x^-4-2x

400

The derivative of f(x)=(5/3)x³-(7/6)x⁶+(6/4)x⁸

What is 5x²-7x⁵+12x⁷

500

The second derivative of f(x)=-5x^-3-(4/3)x^-2

 What is -60x^-5-8x^-4

Product Rule

100

The derivative of f(x) = (4x²-x)(x³-8x²+12)

What is (8x-1)(x³-8x²+12)+(4x²-x)(3x²-16x)

200

The derivative of f(x)=(1+1/x⁵)(3x⁴-2)

What is (1+1/x⁵)(12x³)+(-5x^-6)(3x⁴-2)

300

The second derivative of f(x)=(x²+x+1)(x-1)

What is 6x

400

The derivative of f(x)=(x+1)(sqrt(x)+2)

what is (x+1)/2(sqrt(x)) + sqrt(x) + 2

500

The second derivative of f(x)=xe^x

What is e^x(x+2)

Quotient Rule

100

The derivative of f(x)=(6x²)/(2-x)

What is (24x-6x²)/(2-x)²

200

The derivative of f(x)=(sqrt(x)+2x)/(7x-4x²)

What is (7x-4x²)(1/2x^-1/2+2)-(x^1/2+2x)(7-8x) / (7x-4x²)²

300

The derivative of f(x)=(e^x+e^-x) / 2

What is (e^x-e^-x) / 2

400

The derivative of f(x)= tan(4x) / (x³+2)

What is (x³+2)(4sec²(4x)) - 3x²tan(4x) / (x³+2)²

500

The simplified derivative of f(x)=(2x²-5x)(4x³+7) / 3x²

What is (24x⁴-40x³+35) / 3x²

Random

100

The derivative of f(x) = w⁶ / 5

What is 6/5(w⁵)

200

The derivative of f(x)=12+xcos(x)+x⁵

What is cos(x)+x(-sin(x))+5x⁴

300

The derivative of f(x)=x²sin(5x)

What is 2xsin(5x)+5x²cos(5x)

400

The derivative of f(x)=x(x⁷+15)³

What is 21x⁷(x⁷+15)²

500

The derivative of f(x)= sqrt(1-cosx) * (tanx)³

What is 1/2(1-cosx)^-1/2sinx*(tanx)³ + (1-cosx)^1/2 * 3(tanx)²sec²x