Consider the following statements Statement 1 : If y= ₁₀ x+ _ c x , then d y d x = ₁₀ e x + 1 x Statement 2 : If d d x ( ₁₀ x )= x 10 and d d x ( _ e x )= x e

Step-by-step solution

Statement 1 , aligned y &= ₁₀ x+ _ e x y &= _ e x _ e 10 + _ e x aligned On differentiating w.r.t. x , we get aligned d y d x &= 1 x _ e 10 + 1 x d y d x &= ₁₀ e x + 1 x Statement 2, d d x ₁₀ x &= d d x _ e x _ e 10 &= _ x x _ e 10 d d x ( _ e x ) &= d d x _ e x _ e e = 1 x aligned Hence, statement 1 is true but statement 2 is false.