SI Session #4: 7.7 Review

Derivatives of Hyperbolic Functions

100

The derivative of cosh(4x)

What is 4sinh4(x)?

200

The derivative of coth(5x)

What is -5csch²(5x)?

300

The derivative of tanh(x²)

What is 2xsech²(x²)?

400

The derivative of 1/cosh(4x)

What is -4sech(4x)tanh(4x)?

500

The derivative of sinh(2x)cosh(2x)

What is 2cosh2(2x)+2sinh2(2x)?

Derivatives of Inverse Hyperbolic Functions

100

The derivative of sinh^-1(4x)

What is 4/(1+16x²)^1/2?

200

The derivative of tanh^-1(x³)

What is 3x²/(1-x⁶)?

300

The derivative of ln(sinh^-1(x))

What is 1/(sinh^-1(x)*(1+x²)^1/2)?

400

The derivative of sinh^-1(3x²)

What is 6x/(1+9x⁴)^1/2?

500

The derivative of ln(cosh^-1(x²+2x+2))

What is (2x+2)/(cosh^-1(x²+2x+2)*(x⁴+4x³+8x²+8x+3)^1/2)?

Integrals of Hyperbolic Functions

100

The integral of cosh(5x)

What is 1/5 * sinh(5x) + C?

200

The integral of sinh(4x-1)

What is 1/4 * cosh(4x-1) + C?

300

The integral of (3sinh(x)-2cosh(x))

What is 3cosh(x)-2sinh(x) + C?

400

The integral of cosh²(x)

What is x/2 + 1/4 * sinh(2x) + C?

500

The integral of (sinh(x))/(1+cosh²(x))

What is tan^-1(cosh(x)) + C?

Integrals of Inverse Hyperbolic Functions

100

The integral of 1/(x²+9)^1/2

What is sinh^-1(x/3) + C?

200

The integral of 4/(16x²+1)^1/2

What is sinh^-1(4x) + C?

300

The integral of 3/(9x²+1)^1/2​​​​

What is sinh^-1(3x) + C?

400

The integral of 5/(25x²+9)^1/2

What is 5/3 * sinh^-1(5/3 * x) + C?

500

The integral of (2x+1)/((x²+x+1)²+1)^1/2

What is sinh^-1(x²+x+1) + C?

Identities for Inverse Hyperbolic/Hyperbolic Functions

100

The value of tanh(x) if sinh(x)=4/3

What is 4/5?

200

The value of sech(x) if tanh(x)=4/5

What is 3/5?

300

The value of sech(x) if cosh(x)=17/18

What is 18/17?

400

Simplify cosh(3x)-sinh(3x) using identities

What is e^-3x?

500

Simplify sinh(ln(x²)) using identities

What is (x⁴-1)/2x²?