HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a² + b² + c² .

Differentiate the following w.r.t. x:

(x³ – 2x – 1)⁵

Differentiate the following w.r.t.x:

`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`

Differentiate the following w.r.t. x: `sqrt(x^2 + 4x - 7)`.

Differentiate the following w.r.t.x:

`sqrt(x^2 + sqrt(x^2 + 1)`

Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`

Differentiate the following w.r.t.x:

`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`

Differentiate the following w.r.t.x: cos(x² + a²)

Differentiate the following w.r.t.x:

`sqrt(e^((3x + 2) +  5)`

Differentiate the following w.r.t.x: `log[tan(x/2)]`

Differentiate the following w.r.t.x: `sqrt(tansqrt(x)`

Differentiate the following w.r.t.x: cot³[log(x³)]

Differentiate the following w.r.t.x: `5^(sin^3x + 3)`

Differentiate the following w.r.t.x: `"cosec"(sqrt(cos x))`

Differentiate the following w.r.t.x: log[cos(x³ – 5)]

Differentiate the following w.r.t.x: `e^(3sin^2x - 2cos^2x)`

Differentiate the following w.r.t.x: cos²[log(x² + 7)]

Differentiate the following w.r.t.x:

tan[cos(sinx)]

Differentiate the following w.r.t.x: sec[tan (x⁴ + 4)]

Differentiate the following w.r.t.x: `e^(log[(logx)^2 - logx^2]`